Question: What is the vertex figure of this object?

Instruction: Determine the Wikipedia snippet that matches the question of this image.

Hexagon. of the circumscribed circle or circumcircle, which equals formula_1 times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries ("rotational symmetry of order six") and six reflection symmetries ("six lines of symmetry"), making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon.

Hexagon. adding alternating squares and equilateral triangles around it. This pattern repeats within the rhombitrihexagonal tiling.## Self-crossing hexagons.There are six self-crossing hexagons with the vertex arrangement of the regular hexagon:## Hexagonal structures.From bees' honeycombs to the Giant's Causeway, hexagonal patterns are prevalent in nature due to their efficiency. In a hexagonal grid each line is as short as it can possibly be if a large area is to be filled with the fewest hexagons. This means that honeycombs require less wax to construct and gain much strength under compression.Irregular hexagons with parallel opposite edges are called parallelogons and can also tile.

Hexagon. the plane by translation. In three dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation.## Tesselations by hexagons.In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the Conway criterion will tile the plane.## Hexagon inscribed in a conic section.Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line.

Hexagon. of that configuration.## Cyclic hexagon.The Lemoine hexagon is a cyclic hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.If the successive sides of a cyclic hexagon are "a", "b", "c", "d", "e", "f", then the three main diagonals intersect in a single point if and only if .If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments.

Hexagon. connecting the circumcenters of opposite triangles are concurrent.If a hexagon has vertices on the circumcircle of an acute triangle at the six points (including three triangle vertices) where the extended altitudes of the triangle meet the circumcircle, then the area of the hexagon is twice the area of the triangle.## Hexagon tangential to a conic section.Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then Brianchon's theorem states that the three main diagonals AD, BE, and CF intersect at a single point.In a hexagon that is tangential to a circle and that has consecutive sides.

Hexagon. "a", "b", "c", "d", "e", and "f",formula_16## Equilateral triangles on the sides of an arbitrary hexagon.If an equilateral triangle is constructed externally on each side of any hexagon, then the midpoints of the segments connecting the centroids of opposite triangles form another equilateral triangle.## Skew hexagon.A skew hexagon is a skew polygon with six vertices and edges but not existing on the same plane. The interior of such an hexagon is not generally defined. A "skew zig-zag hexagon" has vertices alternating between two parallel planes.A regular skew hexagon is vertex-transitive with equal edge lengths. In three dimensions it will be.


Question: What is the name of the vessel involved in this event?

Instruction: Retrieve a Wikipedia paragraph that provides an answer to the given query about the image.

Kon-Tiki expedition. The "Kon-Tiki" expedition was a 1947 journey by raft across the Pacific Ocean from South America to the Polynesian islands, led by Norwegian explorer and writer Thor Heyerdahl. The raft was named "Kon-Tiki" after the Inca god Viracocha, for whom "Kon-Tiki" was said to be an old name. "" is also the name of Heyerdahl's book, the Academy Award–winning 1950 documentary film chronicling his adventures, and the 2012 dramatized feature film nominated for the Academy Award for Best Foreign Language Film.Heyerdahl believed that people from South America could have reached Polynesia during pre-Columbian times. His aim in mounting the "Kon-Tiki.

Kon-Tiki expedition. expedition was to show, by using only the materials and technologies available to those people at the time, that there were no technical reasons to prevent them from having done so. Although the expedition carried some modern equipment, such as a radio, watches, charts, sextant, and metal knives, Heyerdahl argued they were incidental to the purpose of proving that the raft itself could make the journey. This idea has recently received support from statistical analysis of genetic evidence of contact between South America and Polynesia.Heyerdahl's full hypothesis of a South American origin of the Polynesian peoples is generally rejected by.

Kon-Tiki expedition. scientists today. Most archaeological, linguistic, cultural, and genetic evidence tends to support a western origin for Polynesians, from Island Southeast Asia, using sophisticated multihull sailing technologies and navigation techniques during the Austronesian expansion. However, there is evidence of some gene flow from South America to Easter Island. In 2020 some researchers published research confirming a wider impact on genetic and cultural elements in Polynesia due to South American contacts. The "Kon-Tiki" expedition was funded by private loans, along with donations of equipment from the United States Army. Heyerdahl and a small team went to Peru, where, with the help of.

Kon-Tiki expedition. dockyard facilities provided by the Peruvian authorities, they constructed the raft out of balsa logs and other native materials in an indigenous style as recorded in illustrations by Spanish conquistadores. The trip began on April 28, 1947. Heyerdahl and five companions sailed the raft for 101 days over 6,900 km (4,300 miles) across the Pacific Ocean before smashing into a reef at Raroia in the Tuamotus on August 7, 1947. The crew made successful landfall and all returned safely.Thor Heyerdahl's book about his experience became a bestseller. It was published in Norwegian in 1948 as "The Kon-Tiki Expedition: By Raft.

Kon-Tiki expedition. Across the South Seas", later reprinted as "Kon-Tiki: Across the Pacific in a Raft". It appeared with great success in English in 1950, also in many other languages. A documentary motion picture about the expedition, also called "Kon-Tiki", was produced from a write-up and expansion of the crew's filmstrip notes and won an Academy Award in 1951. It was directed by Heyerdahl and edited by Olle Nordemar. The voyage was also chronicled in the documentary TV-series "The Kon-Tiki Man: The Life and Adventures of Thor Heyerdahl", directed by Bengt Jonson.The original "Kon-Tiki" raft is now on display in the Kon-Tiki.

Kon-Tiki expedition. Museum at Bygdøy in Oslo.## Crew."Kon-Tiki" had a six-man crew, all of whom were Norwegian except for Bengt Danielsson, a Swede. Thor Heyerdahl (1914–2002) was the expedition leader. He was also the author of the book of the expedition and the narrator of the story. Heyerdahl had studied the ancient people of South America and Polynesia and believed that there was a link between the two. Erik Hesselberg (1914–1972) was the navigator and artist. He painted the large Kon-Tiki figure on the raft's sail. His children's book "Kon-Tiki and I" appeared in Norwegian in 1949 and has since been published.

Kon-Tiki expedition. in more than 15 languages. Bengt Danielsson (1921–1997) took on the role of steward, in charge of supplies and daily rations. Danielsson was a Swedish sociologist interested in human migration theory. He also served as translator, as he was the only member of the crew who spoke Spanish. He was also a voracious reader; his box aboard the raft contained many books. Knut Haugland (1917–2009) was a radio expert, decorated by the British in World War II for actions in the Norwegian heavy water sabotage that stalled what were believed to be Germany's plans to develop an atomic bomb. Haugland.

Kon-Tiki expedition. was the last surviving crew member; he died on Christmas Day, 2009 at the age of 92. Torstein Raaby (1918–1964) was also in charge of radio transmissions. He gained radio experience while hiding behind German lines during WWII, spying on the German battleship "Tirpitz". His secret radio transmissions eventually helped guide in Allied bombers to sink the ship. Herman Watzinger (1910–1986) was an engineer whose area of expertise was in technical measurements. He was the first to join Heyerdahl for the trip. He collected and recorded all sorts of data on the voyage. Much of what he recorded, such as.

Kon-Tiki expedition. weather data, was sent back to various people, since this area of the ocean was largely unstudied.The expedition also carried a pet parrot named Lorita.## Construction.The main body of the float was composed of nine balsa tree trunks up to 45 (ft) long, 2 (ft) in diameter, lashed together with 1+1/4 (in) hemp ropes. Cross-pieces of balsa logs 18 (ft) long and 1 (ft) in diameter were lashed across the logs at 3 (ft) intervals to give lateral support. Pine splashboards clad the bow, and lengths of pine 1 (in) thick and 2 (ft) wide were wedged between the balsa.

Kon-Tiki expedition. logs and used as centreboards.The main mast was made of lengths of mangrove wood lashed together to form an A-frame 29 (ft) high. Behind the main-mast was a cabin of plaited bamboo 14 (ft) long and 8 (ft) wide, about 4 - 5 (ft) high and roofed with banana leaf thatch. At the stern was a 19 (ft) long steering oar of mangrove wood, with a blade of fir. The main sail was 15 by 18 (ft) on a yard of bamboo stems lashed together. Photographs also show a top-sail above the main sail, and also a mizzen-sail, mounted at.

Kon-Tiki expedition. the stern.The raft was partially decked in split bamboo. The main spars were a laminate of wood and reeds and Heyerdahl tested more than twenty different composites before settling on one that proved an effective compromise between bulk and torsional rigidity. No metal was used in the construction.## Supplies."Kon-Tiki" carried 275 (USgal) of drinking water in 56 water cans, as well as a number of sealed bamboo rods. The purpose stated by Heyerdahl for carrying modern and ancient containers was to test the effectiveness of ancient water storage. For food "Kon-Tiki" carried 200 coconuts, sweet potatoes, bottle gourds and other.

Kon-Tiki expedition. assorted fruit and roots. The U.S. Army Quartermaster Corps provided field rations, tinned food and survival equipment. In return, the "Kon-Tiki" explorers reported on the quality and utility of the provisions. They also caught plentiful numbers of fish, particularly flying fish, "dolphin fish", yellowfin tuna, bonito and shark.Heyerdahl and crew were equipped with water-tight sports wristwatches manufactured by Swiss watchmaking firm Eterna. After the journey, Eterna decided to brand their sports watches as "Kon-Tiki".## Communications.The expedition carried an amateur radio station with the call sign of LI2B operated by former World War II Norwegian resistance radio operators Knut Haugland and.

Kon-Tiki expedition. Torstein Raaby. Haugland and Raaby maintained regular communication with a number of American, Canadian, and South American stations that relayed "Kon Tiki's" status to the Norwegian Embassy in Washington, D.C. On August 5, Haugland made contact with a station in Oslo, Norway, 10000 (mi) away."Kon Tiki's" transmitters were powered by batteries and a hand-cranked generator and operated on the 40, 20, 10, and 6-meter bands. Each unit was water resistant, used 2E30 vacuum tubes, and provided approximately 6 watts of RF output; the equivalent of a small flashlight. Two British 3-16 MHz Mark II transmitters were also carried on board,.

Kon-Tiki expedition. as was a VHF transmitter for communicating with aircraft and a hand-cranked survival radio of the Gibson Girl type for 500 and 8280 kHz.The radio receiver used throughout the voyage, a National Radio Company NC-173, once required a thorough drying out after being soaked when landing in Raratonga. The crew once used a hand-cranked emergency transmitter to send out an "all well, all well" message "just in time to head off a massive rescue attempt".The call sign LI2B was used by Heyerdahl again in 1969–70, when he built a papyrus reed raft and sailed from Morocco to Barbados in an.

Kon-Tiki expedition. attempt to show a possible link between the civilization of ancient Egypt and the New World.## The voyage."Kon-Tiki" left Callao, Peru, on the afternoon of April 28, 1947. To avoid coastal traffic it was initially towed 50 (mi) out by the Peruvian Navy fleet tug "Guardian Rios", then sailed roughly west carried along on the Humboldt Current.On 2 July Heyerdahl writes about an encounter with a rogue wave; in his book he describes a "Three Sister" phenomenon: "During a night-shift with quiet seas appears an 'abnormal huge wave' followed by two more waves. The raft is being swept up and.

Kon-Tiki expedition. down and is covered in water." After the three waves he describes the sea as quiet as before.The crew's first sight of land was the atoll of Puka-Puka on July 30. On August 4, the 97th day after departure, "Kon-Tiki" reached the Angatau atoll. The crew made brief contact with the inhabitants of Angatau Island, but were unable to land safely. Calculations made by Heyerdahl before the trip had indicated that 97 days was the minimum amount of time required to reach the Tuamotus, so the encounter with Angatau showed that they had made good time.On August 7, the voyage.

Kon-Tiki expedition. ended when the raft struck a reef and was then beached on an uninhabited islet off Raroia atoll in the Tuamotus. The team had travelled a distance of around 6980 (km) in 101 days, at an average speed of 1.5 (kn).After spending a number of days alone on the islet, the crew was greeted by men from a village on a nearby island who arrived in canoes, having seen washed-up flotsam from the raft. The crew were taken back to the native village, where they were feted with traditional dances and other festivities. Finally the crew were taken off Raroia.

Kon-Tiki expedition. to Tahiti by the French schooner "Tamara", with the salvaged "Kon-Tiki" in tow.## Anthropology.The basis of the "Kon-Tiki" expedition was pseudoscientific, racially controversial, and has not gained acceptance among scientists (even prior to the voyage). Heyerdahl believed that the original inhabitants of Easter Island (and the rest of Polynesia) were the "Tiki people", a race of "white bearded men" who supposedly originally sailed from Peru. He described these "Tiki people" as being a sun-worshipping fair-skinned people with blue eyes, fair or red hair, tall statures, and beards. He further said that these people were originally from the Middle East, and.

Kon-Tiki expedition. had crossed the Atlantic earlier to found the great Mesoamerican civilizations. By 500 CE, a branch of these people were supposedly forced out into Tiahuanaco where they became the ruling class of the Inca Empire and set out to voyage into the Pacific Ocean under the leadership of "Con Ticci Viracocha".He argued that the monumental statues known as moai resembled sculptures more typical of pre-Columbian Peru than any Polynesian designs. He believed that the Easter Island myth of a power struggle between two peoples called the Hanau epe and Hanau momoko was a memory of conflicts between the original inhabitants.

Kon-Tiki expedition. of the island and a later wave of Native Americans from the Northwest coast, eventually leading to the annihilation of the Hanau epe and the destruction of the island's culture and once-prosperous economy. Heyerdahl described these later migrants as "Maori-Polynesians" who were supposedly Asians who crossed over the Bering land bridge into Northwest America before sailing westward towards Polynesia (the westward direction is because he refused to accept that Polynesians were capable of sailing against winds and currents). He associated them with the Tlingit and Haida peoples and characterized them as "inferior" to the Tiki people.Heyerdahl's hypothesis was part of.

Kon-Tiki expedition. early Eurocentric hyperdiffusionism and the westerner disbelief that (non-white) "stone-age" peoples with "no math" could colonize islands separated by vast distances of ocean water, even against prevailing winds and currents. He rejected the highly skilled voyaging and navigating traditions of the Austronesian peoples and instead argued that Polynesia was settled from boats following the wind and currents for navigation from South America. As such, the "Kon-Tiki" was deliberately a primitive raft and unsteerable, in contrast to the sophisticated outrigger canoes and catamarans of the Austronesian people.Heyerdahl's hypothesis of Polynesian origins is overwhelmingly rejected by scientists today. Archaeological, linguistic, cultural, and.

Kon-Tiki expedition. genetic evidence all support a western origin (from Island Southeast Asia) for Polynesians via the Austronesian expansion. "Drift voyaging" from South America was also deemed "extremely unlikely" in 1973 by computer modeling, although is in contrast with recent genetic analysis. The 1976 voyage of the "Hōkūleʻa", a performance-accurate replica of a Polynesian double-hulled "wa'a kaulua" voyaging canoe, from Hawaiʻi to Tahiti was partly a demonstration to prove that Heyerdahl was wrong. The "Hōkūleʻa" sailed against prevailing winds and exclusively used wayfinding and celestial Polynesian navigation techniques (unlike the modern equipment and charts of the "Kon-Tiki"). "Hōkūleʻa" also remains fully operational,.

Kon-Tiki expedition. and has since completed ten other voyages, including a three-year circumnavigation of the planet from 2014 to 2017, with other sister ships.Historians today consider that the Polynesians from the west were the original inhabitants and that the story of the Hanau epe is either pure myth, or a memory of internal tribal or class conflicts. In 2011, Erik Thorsby of the University of Oslo presented DNA evidence to the Royal Society which, whilst agreeing with the west origin, also identified a distinctive but smaller genetic contribution from South America. This result was questioned in 2012 because of the possibility of.

Kon-Tiki expedition. contamination by South Americans after European contact with the islands. In 2014, further work by a team including Anna-Sapfo Malaspinas (from the Natural History Museum of Denmark) analysed the genomes of 27 native Rapa Nui people and found that their DNA was on average 76 percent Polynesian, 8 percent Native American and 16 percent European. Analysis showed that "although the European lineage could be explained by contact with white Europeans after the island was 'discovered' in 1722 by Dutch sailors, the South American component was much older, dating to between about 1280 and 1495, soon after the island was first.

Kon-Tiki expedition. colonised by Polynesians in around 1200." Genetic analysis of Polynesians and Native South Americans, published in "Nature" in July 2020, has revealed that several eastern Polynesian populations have signs of an ancient genetic signature that originated from Native South American people. An initial admixture event between Native South Americans and Polynesians, discovered by statistical analysis, took place around 1150–1230 CE.## Later recreations of "Kon-Tiki".## "Seven Little Sisters".In 1954, William Willis sailed alone on a raft "Seven Little Sisters" from Peru to American Samoa, successfully completing the journey. He sailed 6,700 (mi), which was 2,200 (mi) farther than "Kon-Tiki". In a.

Kon-Tiki expedition. second great voyage ten years later, he rafted 7457 (mi) from South America to Australia with a metal raft "Age Unlimited".## "Kantuta".In 1955, the Czech explorer and adventurer Eduard Ingris attempted to recreate the "Kon-Tiki" expedition on a balsa raft called "Kantuta". His first expedition, "Kantuta I", took place in 1955–1956 and led to failure. In 1959, Ingris built a new balsa raft, "Kantuta II", and tried to repeat the previous expedition. The second expedition was a success. Ingris was able to cross the Pacific Ocean on the balsa raft from Peru to Polynesia.## "Tahiti-Nui".A French seafarer, Éric de Bisschop,.

Kon-Tiki expedition. committed himself in a project he had had for some years: he built a Polynesian raft in order to cross the eastern Pacific Ocean from Tahiti to Chile (contrary to Thor Heyerdahl's crossing); the "Tahiti-Nui" left Papeete with a crew of five on November 8, 1956. When near the Juan Fernández Islands (Chile) in May 1957, the raft was in a very poor state and they asked for a towing, but it was damaged during the operation and had to be abandoned, but they were able to preserve all the equipment that had been aboard.## "Tahiti-Nui II".A second "Tahiti-Nui" was.

Kon-Tiki expedition. built in Constitución, Chile, leaving on April 13, 1958, towards Callao, then towards the Marquesas. It missed its target and after four months, the raft began to sink. The crew built a new smaller raft, the "Tahiti Nui III", in the ocean out of the more buoyant parts of the "Tahiti Nui II". They were swept towards Cook Islands where on August 30, the raft went aground and was wrecked at Rakahanga atoll. Éric de Bisschop died in this accident.## "Tangaroa" (1965).A Peruvian expedition led by Carlos Caravedo crossed the Pacific Ocean in 1965 in 115 days in a raft.

Kon-Tiki expedition. named "Tangaroa", of which 18 days were used by the crew to cross Tuamotus, the Tuamotu Archipielago, making "Tangaroa" the only raft that has managed to cross that dangerous archipelago of French Polynesia by its own means. On November 18, 1965, the "Tangaroa" ended its journey on the Fakarava island. Fakarava is where the "Tangaroa" is currently preserved.## Las Balsas.The 1973 Las Balsas expedition was the first (and so far only) multiple-raft crossing of the Pacific Ocean in recent history. It is the longest-known raft voyage in history. The expedition was led by Spaniard Vital Alsar, who, in 1970, led.

Kon-Tiki expedition. the La Balsa expedition, only on that occasion with one raft and three companions. The crossing was successful and, at the time, the longest raft voyage in history, until eclipsed in 1973 by Las Balsas. The purpose of the 1973 expedition was three-fold: (1) to prove that the success of 1970 was no accident, (2) to test different currents in the sea, which Alsar maintained ancient mariners knew as modern humans know road maps, and (3) to show that the original expeditions, directed perhaps toward trade or colonisation, may have consisted of small fleets of balsa rafts.## "Tangaroa" (2006).In 2006,.

Kon-Tiki expedition. the Tangaroa Expedition recreated the "Kon-Tiki" voyage using a newly built raft, the "Tangaroa", named after the Māori sea-god Tangaroa. Tangaroa's six-man crew was led by Norwegian Torgeir Higraff and included Olav Heyerdahl, grandson of Thor Heyerdahl, Bjarne Krekvik (captain), Øyvin Lauten (executive officer), Swedish Anders Berg (photographer) and Peruvian Roberto Sala. "Tangaroa" was launched on the same day that "Kon-Tiki" had been—April 28—and it reached its destination on July 7, which was 30 days faster than Heyerdahl's Kon-Tiki which had taken 101 days for the voyage. Tangaroa's speed was credited to the proper use of guaras (centerboards).## "An-Tiki".On January.

Kon-Tiki expedition. 30, 2011, "An-Tiki", a raft modeled after "Kon-Tiki", began a 3000 (mi), 70-day journey across the Atlantic Ocean from the Canary Islands to the island of Eleuthera in the Bahamas. The expedition was piloted by four men, aged from 56 to 84 years, led by Anthony Smith. The trip was designed to commemorate the journey in an open boat of survivors from the British steamship "Anglo-Saxon", sunk by the German cruiser "Widder" in 1940. The raft ended its voyage in the Caribbean island of St Maarten, completing its trip to Eleuthera in the following year with Smith and a new.

Kon-Tiki expedition. crew.## "Kon-Tiki2".On 7 November 2015, two teams with two balsa rafts "Rahiti Tane" and "Tupac Yupanqui" left Lima, Peru for Easter Island. Expedition "Kon-Tiki2" got its name because it had 2 crews from many nations: Norway, Russia, UK, Mexico, New Zealand, Sweden, and Peru. It sought to double down on Heyerdahl's voyage by sailing two rafts from South America to Polynesia and then back. Expedition leader was Torgeir Higraff from Tangaroa Expedition (2006). Øyvin Lauten and Kari Skår Dahl were captains on the first leg, while Signe Meling and Ola Borgfjord were captains on the second leg. The raft reached.

Kon-Tiki expedition. Easter Island, but did not complete the return.The two rafts were made of 11 balsa logs and 10 crossbeams held together by 2000 meters (1¼ miles) of natural fiber ropes. Tens of thousands of waves, up to six meters (20') tall, hit the rafts in an El Niño year. This stress for 16 weeks weakened the ropes, but the crew could not replace all of them. On March 3, 2016, all crew members were taken on board the Hokuetsu Ushaka freight ship after 115 days of sailing and 4½ months at sea.## Documentation.## Memoir book.A book documenting the voyage and.

Kon-Tiki expedition. raft was released in 1948 by Thor Heyerdahl, called "".## Documentary film.A film documentary about the voyage and raft was released in 1950, called "Kon-Tiki". It won the 1951 Oscar for Best Documentary Feature.## In popular culture."Kon-Tiki" is a 2012 Norwegian historical dramatized feature film about the 1947 "Kon-Tiki" expedition. It starred Pål Sverre Valheim Hagen as Thor Heyerdahl and was directed by Joachim Rønning and Espen Sandberg. It was the highest-grossing film of 2012 in Norway and the country's most expensive production to date.Episode 5 of the tenth season of HBO's "Curb Your Enthusiasm" features Clive Owen as himself.

Kon-Tiki expedition. in a one-man play entitled "Kon Tiki".Episode 2 of the second season of Apple TV+'s "For All Mankind" mentions a Space Shuttle named Kon-Tiki. Experimental archaeology Polynesian navigation Pre-Columbian transoceanic contact theories Pre-Columbian rafts Chincha culture Hyperdiffusionism Tupac Inca Yupanqui Atlantis Expedition Heyerdahl, Thor; Lyon, F.H. (translator) (1950). "Kon-Tiki: Across the Pacific by Raft". Rand McNally & Company, Chicago, Ill. Hesselberg, Erik (1950). "Kon-Tiki and I : illustrations with text, begun on the Pacific on board the raft "Kon-Tiki" and completed at "Solbakken" in Borre." Allen & Unwin Andersson, Axel (2010) "A Hero for the Atomic Age: Thor Heyerdahl and.

Kon-Tiki expedition. the Kon-Tiki Expedition" (Peter Lang) "Kon-Tiki" Museum National NC-173 receiver Quick Facts: Comparing the Two Rafts: Kon-Tiki and Tangaroa "Azerbaijan International", Vol 14:4 (Winter 2006) Testing Heyerdahl's Theories about Kon-Tiki 60 Years Later: Tangaroa Pacific Voyage (Summer 2006) "Azerbaijan International", Vol 14:4 (Winter 2006) Kon-Tiki in Reverse: The Tahiti-Nui Expedition TV2Sumo WebTV programme "Ekspedisjonen Tangaroa" (Tangaroa Expedition) – Norsk Acali 1973 – expedition by raft across Atlantic Librarything, 2007 Hsu-Fu 1993 – bamboo raft across Pacific (west to east) personal.psu.edu "Kon-Tiki" 1947 Documentary.


Question: Who is the discoverer or inventor of this object?

Instruction: Retrieve a Wikipedia paragraph that provides an answer to the given query about the image.

Fresnel lens. A Fresnel lens ( ; ; or ) is a type of composite compact lens developed by the French physicist Augustin-Jean Fresnel (1788–1827) for use in lighthouses. It has been called "the invention that saved a million ships."The design allows the construction of lenses of large aperture and short focal length without the mass and volume of material that would be required by a lens of conventional design. A Fresnel lens can be made much thinner than a comparable conventional lens, in some cases taking the form of a flat sheet. The simpler dioptric (purely refractive) form of the lens.

Fresnel lens. was first proposed by Count Buffon and independently reinvented by Fresnel. The "catadioptric" form of the lens, entirely invented by Fresnel, has outer elements that use total internal reflection as well as refraction; it can capture more oblique light from a light source and add it to the beam of a lighthouse, making the light visible from greater distances.## Description.The Fresnel lens reduces the amount of material required compared to a conventional lens by dividing the lens into a set of concentric annular sections. An ideal Fresnel lens would have an infinite number of sections. In each section, the overall.

Fresnel lens. thickness is decreased compared to an equivalent simple lens. This effectively divides the continuous surface of a standard lens into a set of surfaces of the same curvature, with stepwise discontinuities between them.In some lenses, the curved surfaces are replaced with flat surfaces, with a different angle in each section. Such a lens can be regarded as an array of prisms arranged in a circular fashion with steeper prisms on the edges and a flat or slightly convex center. In the first (and largest) Fresnel lenses, each section was actually a separate prism. 'Single-piece' Fresnel lenses were later produced, being.

Fresnel lens. used for automobile headlamps, brake, parking, and turn signal lenses, and so on. In modern times, computer-controlled milling equipment (CNC) or 3-D printers might be used to manufacture more complex lenses.Fresnel lens design allows a substantial reduction in thickness (and thus mass and volume of material) at the expense of reducing the imaging quality of the lens, which is why precise imaging applications such as photography usually still use larger conventional lenses.Fresnel lenses are usually made of glass or plastic; their size varies from large (old historical lighthouses, meter size) to medium (book-reading aids, OHP viewgraph projectors) to small (TLR/SLR.

Fresnel lens. camera screens, micro-optics). In many cases they are very thin and flat, almost flexible, with thicknesses in the 1 to 5 (mm) range.Most modern Fresnel lenses consist only of refractive elements. Lighthouse lenses, however, tend to include both refracting and reflecting elements, the latter being "outside" the metal rings seen in the photographs. While the inner elements are sections of refractive lenses, the outer elements are reflecting prisms, each of which performs two refractions and one total internal reflection, avoiding the light loss that occurs in reflection from a silvered mirror.## Lighthouse lens sizes.Fresnel designed six sizes of lighthouse lenses,.

Fresnel lens. divided into four "orders" based on their size and focal length. In modern use, these are classified as first through sixth order. An intermediate size between third and fourth order was added later, as well as sizes above first order and below sixth.A first-order lens has a focal length of 920 (mm) and stands about 2.59 (m) high, and 1.8 (m) wide. The smallest (sixth) order has a focal length of 150 (mm) and a height of 433 (mm).The largest Fresnel lenses are called hyperradiant (or hyper-radial). One such lens was on hand when it was decided to build and.

Fresnel lens. outfit the Makapuu Point Light in Hawaii. Rather than order a new lens, the huge optic construction, 12 (ft) tall and with over a thousand prisms, was used there.## Types.There are two main types of Fresnel lens: "imaging" and "non-imaging". Imaging Fresnel lenses use segments with curved cross-sections and produce sharp images, while non-imaging lenses have segments with flat cross-sections, and do not produce sharp images. As the number of segments increases, the two types of lens become more similar to each other. In the abstract case of an infinite number of segments, the difference between curved and flat segments.

Fresnel lens. disappears.Spherical: A spherical Fresnel lens is equivalent to a simple spherical lens, using ring-shaped segments that are each a portion of a sphere, that all focus light on a single point. This type of lens produces a sharp image, although not quite as clear as the equivalent simple spherical lens due to diffraction at the edges of the ridges.Cylindrical: A cylindrical Fresnel lens is equivalent to a simple cylindrical lens, using straight segments with circular cross-section, focusing light on a single line. This type produces a sharp image, although not quite as clear as the equivalent simple cylindrical lens due.

Fresnel lens. to diffraction at the edges of the ridges.Spot: A non-imaging spot Fresnel lens uses ring-shaped segments with cross sections that are straight lines rather than circular arcs. Such a lens can focus light on a small spot, but does not produce a sharp image. These lenses have application in solar power, such as focusing sunlight on a solar panel. Fresnel lenses may be used as components of Köhler illumination optics resulting in very effective nonimaging optics Fresnel-Köhler (FK) solar concentrators.Linear: A non-imaging linear Fresnel lens uses straight segments whose cross sections are straight lines rather than arcs. These lenses focus.

Fresnel lens. light into a narrow band. They do not produce a sharp image, but can be used in solar power, such as for focusing sunlight on a pipe, to heat the water within.## Uses.## Imaging.Fresnel lenses are used as simple hand-held magnifiers. They are also used to correct several visual disorders, including ocular-motility disorders such as strabismus. Fresnel lenses have been used to increase the visual size of CRT displays in pocket televisions, notably the Sinclair TV80. They are also used in traffic lights.Fresnel lenses are used in left-hand-drive European lorries entering the UK and Republic of Ireland (and vice versa,.

Fresnel lens. right-hand-drive Irish and British trucks entering mainland Europe) to overcome the blind spots caused by the driver operating the lorry while sitting on the wrong side of the cab relative to the side of the road the car is on. They attach to the passenger-side window.Another automobile application of a Fresnel lens is a rear view enhancer, as the wide view angle of a lens attached to the rear window permits examining the scene behind a vehicle, particularly a tall or bluff-tailed one, more effectively than a rear-view mirror alone.Multi-focal Fresnel lenses are also used as a part of retina.

Fresnel lens. identification cameras, where they provide multiple in- and out-of-focus images of a fixation target inside the camera. For virtually all users, at least one of the images will be in focus, thus allowing correct eye alignment.Fresnel lenses have also been used in the field of popular entertainment. The British rock artist Peter Gabriel made use of them in his early solo live performances to magnify the size of his head, in contrast to the rest of his body, for dramatic and comic effect. In the Terry Gilliam film "Brazil", plastic Fresnel screens appear ostensibly as magnifiers for the small CRT.

Fresnel lens. monitors used throughout the offices of the Ministry of Information. However, they occasionally appear between the actors and the camera, distorting the scale and composition of the scene to humorous effect. The Pixar movie Wall-E features a Fresnel lens in the scenes where the protagonist watches the musical Hello, Dolly! magnified on an iPod.## Photography.Canon and Nikon have used Fresnel lenses to reduce the size of telephoto lenses. Photographic lenses that include Fresnel elements can be much shorter than corresponding conventional lens design. Nikon calls the technology "Phase Fresnel".The Polaroid SX-70 camera used a Fresnel reflector as part of its.

Fresnel lens. viewing system.View and large format cameras can utilize a Fresnel lens in conjunction with the ground glass, to increase the perceived brightness of the image projected by a lens onto the ground glass, thus aiding in adjusting focus and composition.## Illumination.High-quality glass Fresnel lenses were used in lighthouses, where they were considered state of the art in the late 19th and through the middle of the 20th centuries; most lighthouses have now retired glass Fresnel lenses from service and replaced them with much less expensive and more durable aerobeacons, which themselves often contain plastic Fresnel lenses. Lighthouse Fresnel lens systems.

Fresnel lens. typically include extra annular prismatic elements, arrayed in faceted domes above and below the central planar Fresnel, in order to catch all light emitted from the light source. The light path through these elements can include an internal reflection, rather than the simple refraction in the planar Fresnel element. These lenses conferred many practical benefits upon the designers, builders, and users of lighthouses and their illumination. Among other things, smaller lenses could fit into more compact spaces. Greater light transmission over longer distances, and varied patterns, made it possible to triangulate a position.Perhaps the most widespread use of Fresnel lenses,.

Fresnel lens. for a time, occurred in automobile headlamps, where they can shape the roughly parallel beam from the parabolic reflector to meet requirements for dipped and main-beam patterns, often both in the same headlamp unit (such as the European H4 design). For reasons of economy, weight, and impact resistance, newer cars have dispensed with glass Fresnel lenses, using multifaceted reflectors with plain polycarbonate lenses. However, Fresnel lenses continue in wide use in automobile tail, marker, and reversing lights.Glass Fresnel lenses also are used in lighting instruments for theatre and motion pictures (see Fresnel lantern); such instruments are often called simply "Fresnels".

Fresnel lens. The entire instrument consists of a metal housing, a reflector, a lamp assembly, and a Fresnel lens. Many Fresnel instruments allow the lamp to be moved relative to the lens' focal point, to increase or decrease the size of the light beam. As a result, they are very flexible, and can often produce a beam as narrow as 7° or as wide as 70°. The Fresnel lens produces a very soft-edged beam, so is often used as a wash light. A holder in front of the lens can hold a colored plastic film ("gel") to tint the light or wire.

Fresnel lens. screens or frosted plastic to diffuse it. The Fresnel lens is useful in the making of motion pictures not only because of its ability to focus the beam brighter than a typical lens, but also because the light is a relatively consistent intensity across the entire width of the beam of light.Aircraft carriers and naval air stations typically use Fresnel lenses in their optical landing systems. The "meatball" light aids the pilot in maintaining proper glide slope for the landing. In the center are amber and red lights composed of Fresnel lenses. Although the lights are always on, the angle.

Fresnel lens. of the lens from the pilot's point of view determines the color and position of the visible light. If the lights appear above the green horizontal bar, the pilot is too high. If it is below, the pilot is too low, and if the lights are red, the pilot is very low.Fresnel lenses are also commonly used in searchlights, spotlights, and flashlights.## Projection.The use of Fresnel lenses for image projection reduces image quality, so they tend to occur only where quality is not critical or where the bulk of a solid lens would be prohibitive. Cheap Fresnel lenses can be.

Fresnel lens. stamped or molded of transparent plastic and are used in overhead projectors and projection televisions.Fresnel lenses of different focal lengths (one collimator, and one collector) are used in commercial and DIY projection. The collimator lens has the lower focal length and is placed closer to the light source, and the collector lens, which focuses the light into the triplet lens, is placed after the projection image (an active matrix LCD panel in LCD projectors). Fresnel lenses are also used as collimators in overhead projectors.## Solar power.Since plastic Fresnel lenses can be made larger than glass lenses, as well as being.

Fresnel lens. much cheaper and lighter, they are used to concentrate sunlight for heating in solar cookers, in solar forges, and in solar collectors used to heat water for domestic use. They can also be used to generate steam or to power a Stirling engine.Fresnel lenses can concentrate sunlight onto solar cells with a ratio of almost 500:1. This allows the active solar-cell surface to be reduced, lowering cost and allowing the use of more efficient cells that would otherwise be too expensive. In the early 21st century, Fresnel reflectors began to be used in concentrating solar power (CSP) plants to concentrate.

Fresnel lens. solar energy. One application was to preheat water at the coal-fired Liddell Power Station, in Hunter Valley Australia.Fresnel lenses can be used to sinter sand, allowing 3D printing in glass.## History.## Forerunners.Augustin-Jean Fresnel was not the first person to focus a lighthouse beam using a lens. That distinction apparently belongs to the London glass-cutter Thomas Rogers, who proposed the idea to Trinity House in 1788. The first Rogers lenses, 53cm in diameter and 14cm thick at the center, were installed at the Old Lower Lighthouse at Portland Bill in 1789. Behind each lamp was a back-coated spherical glass mirror, which.

Fresnel lens. reflected rear radiation back through the lamp and into the lens. Further samples were installed at Howth Baily, North Foreland, and at least four other locations by 1804. But much of the light was wasted by absorption in the glass.Nor was Fresnel the first to suggest replacing a convex lens with a series of concentric annular prisms, to reduce weight and absorption. In 1748, Count Buffon proposed grinding such prisms as steps in a single piece of glass. In 1790 (although secondary sources give the date as 1773 or 1788), the Marquis de Condorcet suggested that it would be easier.

Fresnel lens. to make the annular sections separately and assemble them on a frame; but even that was impractical at the time. These designs were intended not for lighthouses, but for burning glasses. David Brewster, however, proposed a system similar to Condorcet's in 1811, and by 1820 was advocating its use in British lighthouses.## Fresnel's contributions.The French (Commission of Lighthouses) was established by Napoleon in 1811, and placed under the authority of Fresnel's employer, the Corps of Bridges and Roads. As the members of the commission were otherwise occupied, it achieved little in its early years. But on 21 June 1819—three months.

Fresnel lens. after winning the physics of the Academy of Sciences for his celebrated memoir on diffraction—Fresnel was "temporarily" seconded to the commission on the recommendation of François Arago (a member since 1813), to review possible improvements in lighthouse illumination.By the end of August 1819, unaware of the Buffon-Condorcet-Brewster proposal, Fresnel made his first presentation to the commission, recommending what he called ('lenses by steps') to replace the reflectors then in use, which reflected only about half of the incident light. Much to Fresnel's embarrassment, one of the assembled commissioners, Jacques Charles, recalled Buffon's suggestion. However, whereas Buffon's version was biconvex and.

Fresnel lens. in one piece, Fresnel's was plano-convex and made of multiple prisms for easier construction. With an official budget of 500 francs, Fresnel approached three manufacturers. The third, François Soleil, found a way to remove defects by reheating and remolding the glass. Arago assisted Fresnel with the design of a modified Argand lamp with concentric wicks (a concept that Fresnel attributed to Count Rumford), and accidentally discovered that fish glue was heat-resistant, making it suitable for use in the lens. The prototype, finished in March 1820, had a square lens panel 55cm on a side, containing 97 polygonal (not annular) prisms—and.

Fresnel lens. so impressed the Commission that Fresnel was asked for a full eight-panel version. This model, completed a year later in spite of insufficient funding, had panels 76cm square. In a public spectacle on the evening of 13 April 1821, it was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete.Soon after this demonstration, Fresnel published the idea that light, including apparently unpolarized light, consists exclusively of transverse waves, and went on to consider the implications for double refraction and partial reflection.Fresnel acknowledged the British lenses and Buffon's invention in a memoir read on 29 July 1822.

Fresnel lens. and printed in the same year. The date of that memoir may be the source of the claim that Fresnel's lighthouse advocacy began two years later than Brewster's; but the text makes it clear that Fresnel's involvement began no later than 1819.Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by Saint-Gobain, giving eight rotating beams—to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements. This refracted the light to a sloping plane mirror, which then reflected.

Fresnel lens. it horizontally, 7 degrees ahead of the main beam, increasing the duration of the flash. Below the main panels were 128 small mirrors arranged in four rings, stacked like the slats of a louver or Venetian blind. Each ring, shaped like a frustum of a cone, reflected the light to the horizon, giving a fainter steady light between the flashes. The official test, conducted on the unfinished on 20 August 1822, was witnessed by the Commission—and by Louis XVIII and his entourage—from 20 (mi) away. The apparatus was stored at Bordeaux for the winter, and then reassembled at Cordouan Lighthouse.

Fresnel lens. under Fresnel's supervision—in part by Fresnel's own hands. On 25 July 1823, the world's first lighthouse Fresnel lens was lit. As expected, the light was visible to the horizon, more than 20 (mi) out.The day before the test of the Cordouan lens in Paris, a committee of the Academy of Sciences reported on Fresnel's memoir and supplements on double refraction—which, although less well known to modern readers than his earlier work on diffraction, struck a more decisive blow for the wave theory of light. Between the test and the reassembly at Cordouan, Fresnel submitted his papers on photoelasticity (16 September.

Fresnel lens. 1822), elliptical and circular polarization and optical rotation (9 December), and partial reflection and total internal reflection (7 January 1823), essentially completing his reconstruction of physical optics on the transverse wave hypothesis. Shortly after the Cordouan lens was lit, Fresnel started coughing up blood.In May 1824, Fresnel was promoted to Secretary of the , becoming the first member of that body to draw a salary, albeit in the concurrent role of Engineer-in-Chief. Late that year, being increasingly ill, he curtailed his fundamental research and resigned his seasonal job as an examiner at the , in order to save his remaining.

Fresnel lens. time and energy for his lighthouse work.In the same year he designed the first "fixed" lens—for spreading light evenly around the horizon while minimizing waste above or below. Ideally the curved refracting surfaces would be segments of toroids about a common vertical axis, so that the dioptric panel would look like a cylindrical drum. If this was supplemented by reflecting (catoptric) rings above and below the refracting (dioptric) parts, the entire apparatus would look like a beehive. The second Fresnel lens to enter service was indeed a fixed lens, of third order, installed at Dunkirk by 1 February 1825. However,.

Fresnel lens. due to the difficulty of fabricating large toroidal prisms, this apparatus had a 16-sided polygonal plan.In 1825 Fresnel extended his fixed-lens design by adding a rotating array outside the fixed array. Each panel of the rotating array was to refract part of the fixed light from a horizontal fan into a narrow beam.Also in 1825, Fresnel unveiled the ('lighthouse map'), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes called "orders" (the first being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per.

Fresnel lens. minute (from a rotating lens with eight panels), and two per minute (16 panels).In late 1825, to reduce the loss of light in the reflecting elements, Fresnel proposed to replace each mirror with a catadioptric prism, through which the light would travel by refraction through the first surface, then total internal reflection off the second surface, then refraction through the third surface. The result was the lighthouse lens as we now know it. In 1826 he assembled a small model for use on the , but he did not live to see a full-sized version: he died on 14 July.

Fresnel lens. 1827, at the age of 39.## After Fresnel.The first stage of the development of lighthouse lenses after the death of Augustin Fresnel consisted in the implementation of his designs. This was driven in part by his younger brother Léonor—who, like Augustin, was trained as a civil engineer but, unlike Augustin, had a strong aptitude for management. Léonor entered the service of the Lighthouse Commission in 1825, and went on to succeed Augustin as Secretary.The first fixed lens to be constructed with toroidal prisms was a first-order apparatus designed by the Scottish engineer Alan Stevenson under the guidance of Léonor Fresnel,.

Fresnel lens. and fabricated by Isaac Cookson & Co. using French glass; it entered service at the Isle of May, Scotland, on 22 September 1836. The first large catadioptric lenses were made in 1842 for the lighthouses at Gravelines and Île Vierge, France; these were fixed third-order lenses whose catadioptric rings (made in segments) were one metre in diameter. Stevenson's first-order Skerryvore lens, lit in 1844, was only partly catadioptric; it was similar to the Cordouan lens except that the lower slats were replaced by French-made catadioptric prisms, while mirrors were retained at the top. The first "fully" catadioptric first-order lens, installed.

Fresnel lens. at Pointe d'Ailly in 1852, also gave eight rotating beams plus a fixed light at the bottom; but its top section had eight catadioptric panels focusing the light about 4 degrees ahead of the main beams, in order to lengthen the flashes. The first fully catadioptric lens with "purely revolving" beams—also of first order—was installed at Saint-Clément-des-Baleines in 1854, and marked the completion of Augustin Fresnel's original "Carte des Phares".Thomas Stevenson (younger brother of Alan) went a step beyond Fresnel with his "holophotal" lens, which focused the light radiated by the lamp in nearly all directions, forward or backward, into.

Fresnel lens. a single beam. The first version, described in 1849, consisted of a standard Fresnel bull's-eye lens, a paraboloidal reflector, and a rear hemispherical reflector (functionally equivalent to the Rogers mirror of 60 years earlier, except that it subtended a whole hemisphere). Light radiated into the forward hemisphere but missing the bull's-eye lens was deflected by the paraboloid into a parallel beam surrounding the bull's-eye lens, while light radiated into the backward hemisphere was reflected back through the lamp by the spherical reflector (as in Rogers' arrangement), to be collected by the forward components. The first unit was installed at North.

Fresnel lens. Harbour, Peterhead, in August 1849. Stevenson called this version a "catadioptric holophote", although each of its elements was either purely reflective or purely refractive. In the second version of the holophote concept, the bull's-eye lens and paraboloidal reflector were replaced by a catadioptric Fresnel lens—as conceived by Fresnel, but expanded to cover the whole forward hemisphere. The third version, which Stevenson confusingly called a "dioptric holophote", was more innovative: it retained the catadioptric Fresnel lens for the front hemisphere, but replaced the rear hemispherical reflector with a hemispherical array of annular prisms, each of which used "two" total internal reflections.

Fresnel lens. to turn light diverging from the center of the hemisphere back toward the center. The result was an all-glass holophote, with no losses from metallic reflections.James Timmins Chance modified Thomas Stevenson's all-glass holophotal design by arranging the double-reflecting prisms about a vertical axis. The prototype was shown at the 1862 International Exhibition in London. Later, to ease manufacturing, Chance divided the prisms into segments, and arranged them in a cylindrical form while retaining the property of reflecting light from a single point back to that point. Reflectors of this form, paradoxically called "dioptric mirrors", proved particularly useful for returning light.

Fresnel lens. from the landward side of the lamp to the seaward side.As lighthouses proliferated, they became harder to distinguish from each other, leading to the use of colored filters, which wasted light. In 1884, John Hopkinson eliminated the need for filters by inventing the "group-flashing" lens, in which the dioptric and/or the catadioptric panels were split so as to give multiple flashes—allowing lighthouses to be identified not only by frequency of flashes, but also by multiplicity of flashes. Double-flashing lenses were installed at Tampico (Mexico) and Little Basses (Sri Lanka) in 1875, and a triple-flashing lens at Casquets Lighthouse (Channel Islands).

Fresnel lens. in 1876. The example shown (right) is the double-flashing lens of the Point Arena Light, which was in service from 1908 to 1977.The development of hyper-radial lenses was driven in part by the need for larger light sources, such as gas lights with multiple jets, which required a longer focal length for a given beam-width, hence a larger lens to collect a given fraction of the generated light. The first hyper-radial lens was built for the Stevensons in 1885 by F. Barbier & Cie of France, and tested at South Foreland Lighthouse with various light sources. Chance Brothers (Hopkinson's employers).

Fresnel lens. then began constructing hyper-radials, installing their first at Bishop Rock Lighthouse in 1887. In the same year, Barbier installed a hyper-radial at Tory Island. But only about 30 hyper-radials went into service before the development of more compact bright lamps rendered such large optics unnecessary (see "Hyperradiant Fresnel lens").Production of one-piece stepped dioptric lenses—roughly as envisaged by Buffon—became feasible in 1852, when John L. Gilliland of the Brooklyn Flint-Glass Company patented a method of making lenses from pressed and molded glass. The company made small bull's-eye lenses for use on railroads, steamboats, and docks; such lenses were common in the.

Fresnel lens. United States by the 1870s. In 1858 the company produced "a very small number of pressed flint-glass sixth-order lenses" for use in lighthouses—the first Fresnel lighthouse lenses made in America. By the 1950s, the substitution of plastic for glass made it economic to use Fresnel lenses as condensers in overhead projectors. Fresnel imager Fresnel zone plate Lenticular lens Linear Fresnel reflector Prism lighting − Fresnel anidolic optics M. Born and E. Wolf, "Principles of Optics", 7th Ed., Cambridge, 1999. G.-A. Boutry, 1948, "Augustin Fresnel: His time, life and work, 1788–1827", "Science Progress", vol. 36, no. 144 (October 1948), pp. 587–604;.

Fresnel lens. jstor.org/stable/43413515. J.Z. Buchwald, 1989, "The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century", University of Chicago Press, . J. Elton, 2009, "A Light to Lighten our Darkness: Lighthouse Optics and the Later Development of Fresnel's Revolutionary Refracting Lens 1780–1900", "International Journal for the History of Engineering & Technology", vol. 79, no. 2 (July 2009), pp. 183–244; . A. Fresnel, 1822, "Mémoire sur un nouveau système d'éclairage des phares", read 29 July 1822; reprinted in Fresnel, 1866–70, vol. 3, pp. 97–126; translated by T. Tag as "Memoir upon a new system of lighthouse.

Fresnel lens. illumination", U.S. Lighthouse Society, accessed 26 August 2017; archived 19 August 2016. (Cited page numbers refer to the translation.) A. Fresnel (ed. H. de Sénarmont, E. Verdet, and L. Fresnel), 1866–70, "Oeuvres complètes d'Augustin Fresnel" (3 vols.), Paris: Imprimerie Impériale; vol. 1 (1866), vol. 2 (1868), vol. 3 (1870). T.H. Levitt, 2013, "A Short Bright Flash: Augustin Fresnel and the Birth of the Modern Lighthouse", New York: W.W. Norton, . T. Young (ed. G. Peacock), 1855, "Miscellaneous Works of the late Thomas Young", London: J. Murray, vol. 1. "The Fresnel Lens", "The Keeper's Log", Winter 1985, pp. 12–14. U.S. Coast.

Fresnel lens. Guard, "Aids to Navigation", Washington, DC: U.S. Government Printing Office, 1945. U.S. Coast Guard, "Lighthouses, Lenses, Illuminants, Engineering, & Augustin Fresnel: A Historical Bibliography on Works Published Through 2007". United States Lighthouse Society, especially "Fresnel Lenses". W.A. Britten, "The Fresnel lens" (with photographs). J. Francis, "Fresnel Lens - Maxwell Simulation", 13 April 2009. J. Hare, "How the Fresnel lens works" (5-minute video), Vega Science Trust, 2008.


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Convenience. effects.## Health care.Some of the major improvements over the past century has been in improved health care. For example, modern medicine has made leaps in preventing infectious diseases in part due to improved water and sewage treatment. This is obvious in the marked rises in life expectancy.## Technological advancement in underdeveloped countries.Some of the most dramatic technological benefits are seen in underdeveloped countries. For instance, cabling for landline telephone service is expensive and requires a lot of time to complete, especially in the most remote areas. Introduction of cellphone service, on the other hand, is much cheaper and dramatically improves.


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Mshatta Facade. The Mshatta Facade is the decorated part of the facade of the 8th-century Umayyad residential palace of Qasr Mshatta, one of the Desert Castles of Jordan, which is now installed in the south wing of the Pergamon Museum in Berlin, Germany. It is part of the permanent exhibition of the Pergamon Museum of Islamic Art dedicated to Islamic art from the 8th to the 19th centuries. This was only a relatively small section of the full length of the facade, surrounding the main entrance; most of the wall was undecorated and remains "in situ".## History.The facade belonged to the Qasr.

Mshatta Facade. in the Pergamon Museum. It was seriously damaged during the Second World War and the bombardment of Berlin. Today, it is one of the most important exhibits of the "Museum für Islamische Kunst" in the Pergamon Museum, and a key monument of early Islamic art and architecture, demonstrating early forms of the arabesque, millefleur and also animals carved in relief.There has been much discussion of the fact that the decoration on the left side of the facade contains many animals among the foliar forms, while on the right of the entranceway in the centre there are no animals. It has.

Mshatta Facade. been suggested that this is because the right-hand side was the outside wall of the mosque.Islamic architectureGrabar, Oleg "The Date and Meaning of Mshatta" Dumbarton Oaks Papers, Vol. 41, Studies on Art and Archeology in Honor of Ernst Kitzinger on His Seventy-Fifth Birthday (1987), pp. 243–247 Enderlein, Volkmar "Mshatta-A Caliphs Palace" The Pergamon Museum Information leaflet No. ISL I, Berlin, 1996The Date and Meaning of Mshatta.


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30 St Mary Axe. 30 St Mary Axe (previously known as the Swiss Re Building and informally known as the Gherkin) is a commercial skyscraper in London's primary financial district, the City of London. It was completed in December 2003 and opened in April 2004. With 41 floors, it is 180 (m) tall and stands on the sites of the former Baltic Exchange and Chamber of Shipping, which were extensively damaged in 1992 in the Baltic Exchange bombing by a device placed by the Provisional IRA in St Mary Axe, a narrow street leading north from Leadenhall Street.After plans to build the 92-storey Millennium.

30 St Mary Axe. Tower were dropped, 30 St Mary Axe was designed by Norman Foster and the Arup Group. It was erected by Skanska; construction started in 2001.The building has become a recognisable landmark of London, and it is one of the city's most widely recognised examples of contemporary architecture. It won the 2003 Emporis Skyscraper Award.## Site and early plans.The building stands on the site of the former Baltic Exchange (24–28 St Mary Axe), which was the headquarters of a global marketplace for shipping freight contracts and soft commodities, and the Chamber of Shipping (30–32 St Mary Axe). The tower's topmost panoramic.

30 St Mary Axe. dome, known as the "lens", recalls the iconic glass dome that covered part of the ground floor of the Baltic Exchange and much of which is now displayed at the National Maritime Museum. "The Gherkin" nickname was applied to the current building at least as early as 1999, referring to the plan's highly unorthodox layout and appearance.On 10 April 1992, the Provisional IRA detonated a bomb close to the Baltic Exchange, causing extensive damage to the historic building and neighbouring structures. The United Kingdom government's statutory adviser on the historic environment, English Heritage, and the City of London's governing body,.

30 St Mary Axe. the City of London Corporation, were keen that any redevelopment must restore the Baltic Exchange's old façade onto St Mary Axe. The Exchange Hall was a celebrated fixture of the shipping market.English Heritage then discovered that the damage was far more severe than initially thought, and they stopped insisting on full restoration, albeit over the objections of architectural conservationists. The Baltic Exchange and the Chamber of Shipping sold the land to Trafalgar House in 1995. Most of the remaining structures on the Baltic Exchange site were then carefully dismantled, and the interior of Exchange Hall and the façade were preserved,.

30 St Mary Axe. hoping for a reconstruction of the building in the future. The salvaged material was eventually sold for £800,000 and moved to Tallinn, Estonia, where it awaits reconstruction as the centrepiece of the city's commercial sector.In 1996, Trafalgar House submitted plans for the London Millennium Tower, a 386 (m) building with more than 140000 (sqm) of office space, apartments, shops, restaurants and gardens. This plan was dropped after objections that it was totally out-of-scale in the City of London, and anticipated disruption to flight paths for both London City and London Heathrow airports; the revised plan for a lower tower was.

30 St Mary Axe. accepted.## Planning process.John Prescott, the Deputy Prime Minister, granted planning permission on 23 August 2000 to construct a building on the site, which would be much larger than the old Exchange. The site needed development, was not on any of the "sight lines" (planning guidance requires that new buildings do not obstruct or detract from the view of St Paul's Cathedral dome when viewed from a number of locations around London), and had housed the Baltic Exchange.The plan for the site was to reconstruct the Baltic Exchange. GMW Architects proposed a new rectangular building surrounding a restored exchange: it would.

30 St Mary Axe. have the type of large floor plan that banks liked. Eventually, the planners realised that the exchange was not recoverable, forcing them to relax their building constraints; they hinted that an "architecturally significant" building might obtain a favourable reception from City authorities. This gave the architect a free hand in the design. The building was designed according to the client's needs, rather than for the needs of a large, capital-efficient, money-making building.The new building's low-level plan satisfied the planning authority's desire to maintain London's traditional streetscape, with its narrow streets. The massing of the tower was not too imposing. Like.

30 St Mary Axe. Barclays' former city headquarters in Lombard Street, the idea was that the passer-by in neighbouring streets would be nearly oblivious to the tower's existence until directly underneath it.## Design and construction.The building was constructed by Skanska, completed in December 2003 and opened on 28 April 2004. The primary occupant of the building is Swiss Re, a global reinsurance company, which had the building commissioned as the head office for its UK operation. The tower is thus sometimes known as the Swiss Re Building, although this name has never been official and was never in popular usage anyway, unlike the Gherkin.

30 St Mary Axe. moniker.The building uses energy-saving methods which allow it to use only half the power that a similar tower would typically consume. Gaps in each floor create six shafts that serve as a natural ventilation system for the entire building, even though required firebreaks on every sixth floor interrupt the "chimney". The shafts create a giant double glazing effect; air is sandwiched between two layers of glazing and insulates the office space inside.Architects promote double glazing in residential houses, which avoids the inefficient convection of heat across the relatively narrow gap between the panes, but the tower exploits this effect. The.

30 St Mary Axe. shafts pull warm air out of the building during the summer and warm the building in the winter using passive solar heating. The shafts also allow sunlight to pass through the building, making the work environment more pleasing, and keeping the lighting costs down.The primary methods for controlling wind-excited sways are to increase the stiffness, or increase damping with tuned/active mass dampers. To a design by Arup, its fully triangulated perimeter structure makes the building rigid enough without any extra reinforcements. Despite its overall curved glass shape, there is only one piece of curved glass on the building, the lens-shaped.

30 St Mary Axe. cap at the apex.On the building's top level (the 40th floor), there is a bar for tenants and their guests, with a panoramic view of London. A restaurant operates on the 39th floor, and private dining rooms on the 38th. Most buildings have extensive lift equipment on the roof of the building, but this was not possible for the Gherkin, since a bar had been planned for the 40th floor. The architects dealt with this by having the main lift only reach the 34th floor, with a separate push-from-below lift to the 39th floor. There is a marble stairwell and.

30 St Mary Axe. a disabled persons' lift, which leads the visitor up to the bar in the dome.The building is visible over long distances: From the north, for instance, it can be seen from the M11 motorway, some 32 (km) away, while to the west it can be seen from the statue of George III in Windsor Great Park.## After completion.In April 2005, a glass panel two thirds up the tower fell to the plaza beneath. The plaza was sealed off, but the building remained open. A temporary covered walkway, extending across the plaza to the building's reception, was erected to protect visitors.

30 St Mary Axe. Engineers examined the other 744 glass panels on the building. The cost of repair was covered by main contractor Skanska and curtain-wall supplier Schmidlin (now called Schmidlin-TSK AG). The open-floor ventilation system did not operate as designed due to tenants adding glass partitions to increase security.Since its completion, the building has won a number of awards for architecture. In October 2004, the architect was awarded the 2004 Stirling Prize. For the first time in the prize's history, the judges were unanimous. In December 2005, a survey of the world's largest firms of architects published in "2006 BD World Architecture 200.

30 St Mary Axe. voted the tower as the most admired new building in the world. However, Ken Shuttleworth, who worked for Foster + Partners on the design of the building, said in 2011 that he believed the style was now out-moded: "I was looking at the glass all around and [thought], 'Why on earth did we do that?' Now we would do things differently". The building appeared in recent films such as "Harry Potter and the Half Blood Prince", "A Good Year", "Basic Instinct 2", and "Match Point" and, rechristened the "Spirit of London", became the spaceship centrepiece of Keith Mansfield's 2008 novel.

30 St Mary Axe. "Johnny Mackintosh and the Spirit of London".In September 2006, the building was put up for sale with a price tag of £600 million. Potential buyers included British Land, Land Securities, Prudential, ING, and the Abu Dhabi royal family. On 21 February 2007, IVG Immobilien AG and UK investment firm Evans Randall completed their joint purchase of the building for £630 million, making it Britain's most expensive office building. Swiss Re made a gain of more than £300 million from the sale. The new owners are seeking compensation from four of their former managers on the deal, in which about £620.

30 St Mary Axe. million was paid for a building with a build cost of about £200 million, giving the previous owners a clear £300 million profit.Since February 2010, Sky News has broadcast its flagship business programme, "Jeff Randall Live", from a studio in the building. The top two floors of the tower have been available since at least 2015 for private hire for events.Deloitte announced in April 2014 that the building was again being put up for sale, with an expected price of £550 million. The current owners could not afford to make loan repayments, citing differences in the value of the multi-currency.

30 St Mary Axe. loan and the British pound, high interest rates and general financing structure. In November 2014, the Gherkin was purchased for £700 million by the Safra Group, controlled by the Brazilian billionaire Joseph Safra. Landmarks of London Diagrid List of tallest buildings and structures in London Mathematics and architecture Phallic architecture, a list of similarly shaped buildings that includes 30 St Mary Axe Norman Foster's site about the project.


Question: What is the typical diameter (in 1) of this object?

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Tetrahedron. regular tetrahedron.The following Cartesian coordinates define the four vertices of a tetrahedron with edge length 2, centered at the origin, and two level edges:formula_1Expressed symmetrically as 4 points on the unit sphere, centroid at the origin, with lower face level, the vertices are:formula_2formula_3formula_4formula_5with the edge length of formula_6.Still another set of coordinates are based on an alternated cube or demicube with edge length 2. This form has Coxeter diagram and Schläfli symbol h{4,3}. The tetrahedron in this case has edge length 2. Inverting these coordinates generates the dual tetrahedron, and the pair together form the stellated octahedron, whose vertices are.

Tetrahedron. those of the original cube.Tetrahedron: (1,1,1), (1,−1,−1), (−1,1,−1), (−1,−1,1)Dual tetrahedron: (−1,−1,−1), (−1,1,1), (1,−1,1), (1,1,−1)## Angles and distances.For a regular tetrahedron of edge length "a":With respect to the base plane the slope of a face (2) is twice that of an edge (), corresponding to the fact that the "horizontal" distance covered from the base to the apex along an edge is twice that along the median of a face. In other words, if "C" is the centroid of the base, the distance from "C" to a vertex of the base is twice that from "C" to the midpoint of an.

Tetrahedron. two tetrahedra in the cube). The symmetries of a regular tetrahedron correspond to half of those of a cube: those that map the tetrahedra to themselves, and not to each other.The tetrahedron is the only Platonic solid that is not mapped to itself by point inversion.The regular tetrahedron has 24 isometries, forming the symmetry group Td, [3,3], (*332), isomorphic to the symmetric group, "S"4. They can be categorized as follows: T, [3,3]+, (332) is isomorphic to alternating group, "A"4 (the identity and 11 proper rotations) with the following conjugacy classes (in parentheses are given the permutations of the vertices, or.

Tetrahedron. correspondingly, the faces, and the unit quaternion representation): identity (identity; 1) rotation about an axis through a vertex, perpendicular to the opposite plane, by an angle of ±120°: 4 axes, 2 per axis, together , etc.; ) rotation by an angle of 180° such that an edge maps to the opposite edge: , etc.; ) reflections in a plane perpendicular to an edge: 6 reflections in a plane combined with 90° rotation about an axis perpendicular to the plane: 3 axes, 2 per axis, together 6; equivalently, they are 90° rotations combined with inversion (x is mapped to −x): the.

Tetrahedron. are projected as circular arcs on the plane.## Helical stacking.Regular tetrahedra can be stacked face-to-face in a chiral aperiodic chain called the Boerdijk–Coxeter helix. In four dimensions, all the convex regular 4-polytopes with tetrahedral cells (the 5-cell, 16-cell and 600-cell) can be constructed as tilings of the 3-sphere by these chains, which become periodic in the three-dimensional space of the 4-polytope's boundary surface.## Irregular tetrahedra.Tetrahedra which do not have four equilateral faces are categorized and named by the symmetries they do possess.If all three pairs of opposite edges of a tetrahedron are perpendicular, then it is called an orthocentric tetrahedron.

Tetrahedron. to the opposite faces are inversely proportional to the areas of these faces.For a tetrahedron with vertices,, and, the volume is , or any other combination of pairs of vertices that form a simply connected graph. This can be rewritten using a dot product and a cross product, yieldingformula_9If the origin of the coordinate system is chosen to coincide with vertex d, then d = 0, soformula_10where a, b, and c represent three edges that meet at one vertex, and is a scalar triple product. Comparing this formula with that used to compute the volume of a parallelepiped, we conclude.

Tetrahedron. that the volume of a tetrahedron is equal to of the volume of any parallelepiped that shares three converging edges with it.The absolute value of the scalar triple product can be represented as the following absolute values of determinants:formula_11orformula_12whereformula_13are expressed as row or column vectors.Henceformula_14whereformula_15which givesformula_16where "α", "β", "γ" are the plane angles occurring in vertex d. The angle "α", is the angle between the two edges connecting the vertex d to the vertices b and c. The angle "β", does so for the vertices a and c, while "γ", is defined by the position of the vertices a and.

Tetrahedron. b.If we do not require that d = 0 thenformula_17Given the distances between the vertices of a tetrahedron the volume can be computed using the Cayley–Menger determinant:formula_18where the subscripts represent the vertices and "d" is the pairwise distance between them – i.e., the length of the edge connecting the two vertices. A negative value of the determinant means that a tetrahedron cannot be constructed with the given distances. This formula, sometimes called Tartaglia's formula, is essentially due to the painter Piero della Francesca in the 15th century, as a three dimensional analogue of the 1st century Heron's formula for the.

Tetrahedron. area of a triangle.Let be three edges that meet at a point, and the opposite edges. Let be the volume of the tetrahedron; thenformula_19whereformula_20The above formula uses six lengths of edges, and the following formula uses three lengths of edges and three angles.formula_21## Heron-type formula for the volume of a tetrahedron.If , , , , , are lengths of edges of the tetrahedron (first three form a triangle; with opposite , opposite , opposite ), thenformula_22where formula_23 formula_24## Volume divider.Any plane containing a bimedian (connector of opposite edges' midpoints) of a tetrahedron bisects the volume of the tetrahedron.## Non-Euclidean volume.For.

Tetrahedron. segment joining the midpoints of two opposite edges is called a "bimedian" of the tetrahedron. Hence there are four medians and three bimedians in a tetrahedron. These seven line segments are all concurrent at a point called the "centroid" of the tetrahedron. In addition the four medians are divided in a 3:1 ratio by the centroid (see Commandino's theorem). The centroid of a tetrahedron is the midpoint between its Monge point and circumcenter. These points define the "Euler line" of the tetrahedron that is analogous to the Euler line of a triangle.The nine-point circle of the general triangle has an.

Tetrahedron. is a diagonal of one of the cube's faces. For one such embedding, the Cartesian coordinates of the vertices are(+1, +1, +1);(−1, −1, +1);(−1, +1, −1);(+1, −1, −1).This yields a tetrahedron with edge-length 2, centered at the origin. For the other tetrahedron (which is dual to the first), reverse all the signs. These two tetrahedra's vertices combined are the vertices of a cube, demonstrating that the regular tetrahedron is the 3-demicube.The volume of this tetrahedron is one-third the volume of the cube. Combining both tetrahedra gives a regular polyhedral compound called the compound of two tetrahedra or stella octangula.The interior.

Tetrahedron. of the stella octangula is an octahedron, and correspondingly, a regular octahedron is the result of cutting off, from a regular tetrahedron, four regular tetrahedra of half the linear size (i.e., rectifying the tetrahedron).The above embedding divides the cube into five tetrahedra, one of which is regular. In fact, five is the minimum number of tetrahedra required to compose a cube. To see this, starting from a base tetrahedron with 4 vertices, each added tetrahedra adds at most 1 new vertex, so at least 4 more must be added to make a cube, which has 8 vertices.Inscribing tetrahedra inside the.

Tetrahedron. and counterclockwise orientations of the surface.Putting any of the four vertices in the role of "O" yields four such identities, but at most three of them are independent: If the "clockwise" sides of three of them are multiplied and the product is inferred to be equal to the product of the "counterclockwise" sides of the same three identities, and then common factors are cancelled from both sides, the result is the fourth identity.Three angles are the angles of some triangle if and only if their sum is 180° (π radians). What condition on 12 angles is necessary and sufficient for.

Tetrahedron. them to be the 12 angles of some tetrahedron? Clearly the sum of the angles of any side of the tetrahedron must be 180°. Since there are four such triangles, there are four such constraints on sums of angles, and the number of degrees of freedom is thereby reduced from 12 to 8. The four relations given by this sine law further reduce the number of degrees of freedom, from 8 down to not 4 but 5, since the fourth constraint is not independent of the first three. Thus the space of all shapes of tetrahedra is 5-dimensional.## Law of.

Tetrahedron. faces are "F"a, "F"b, "F"c, and "F"d. Thenformula_29For vertices "A", "B", "C", and "D", interior point "P", and feet "J", "K", "L", and "M" of the perpendiculars from "P" to the faces, and suppose the faces have equal areas, thenformula_30## Inradius.Denoting the inradius of a tetrahedron as "r" and the inradii of its triangular faces as "r""i" for "i" = 1, 2, 3, 4, we haveformula_31with equality if and only if the tetrahedron is regular.If "A""1", "A""2", "A""3" and "A""4" denote the area of each faces, the value of "r" is given byformula_32.This formula is obtained from dividing the tetrahedron.

Tetrahedron. tetrahedra. One example has one edge of 896, the opposite edge of 990 and the other four edges of 1073; two faces are isosceles triangles with areas of and the other two are isosceles with areas of , while the volume is .A tetrahedron can have integer volume and consecutive integers as edges, an example being the one with edges 6, 7, 8, 9, 10, and 11 and volume 48.## Related polyhedra and compounds.A regular tetrahedron can be seen as a triangular pyramid.A regular tetrahedron can be seen as a degenerate polyhedron, a uniform "digonal antiprism", where base polygons are.

Tetrahedron. is arccos(−), or approximately 109.47°.Water, , also has a tetrahedral structure, with two hydrogen atoms and two lone pairs of electrons around the central oxygen atoms. Its tetrahedral symmetry is not perfect, however, because the lone pairs repel more than the single O–H bonds.Quaternary phase diagrams of mixtures of chemical substances are represented graphically as tetrahedra.However, quaternary phase diagrams in communication engineering are represented graphically on a two-dimensional plane.## Electricity and electronics.If six equal resistors are soldered together to form a tetrahedron, then the resistance measured between any two vertices is half that of one resistor.Since silicon is the most.

Tetrahedron. rolled appearing around the bottom or on the top vertex. Some Rubik's Cube-like puzzles are tetrahedral, such as the Pyraminx and Pyramorphix.## Geology.The tetrahedral hypothesis, originally published by William Lowthian Green to explain the formation of the Earth, was popular through the early 20th century.## Weaponry.Some caltrops are based on tetrahedra as one spike points upwards regardless of how they land and can be easily made by welding two bent nails together.## Contemporary art.The Austrian artist Martina Schettina created a tetrahedron using fluorescent lamps. It was shown at the light art biennale Austria 2010.It is used as album artwork, surrounded.


Question: What is the closest parent taxonomy of this plant?

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Securigera varia. Securigera varia (synonym Coronilla varia), commonly known as crownvetch or purple crown vetch, is a low-growing legume vine. It is native to Africa, Asia and Europe and is commonly used throughout the United States and Canada for erosion control, roadside planting and soil rehabilitation. It has become an invasive species in many states of the US.Crownvetch grows 1 to 2 feet tall and bears small clusters of 1/2-inch pink and white flowers from early summer to late fall. The variety Penngift produces mounds of pink flowers. Crownvetch is a tough, aggressive spreading plant that will crowd out its neighbors in.

Securigera varia. a show garden but is well suited to a sunny bank, where it will grow for decades with little to no fertilizing, mowing, or weeding since the thick foliage prevents weeds from growing amid it. Its deep, tenacious, complex root system and thick, fern-like leaves provide excellent erosion control where it is used as a ground cover. However, this legume has a very long germination period of about 6 months and does not create full coverage until two or three years later.## Forage.Crownvetch is toxic to horses and other non-ruminants because of the presence of nitroglycosides. If consumed in large.

Securigera varia. amounts, it can cause slow growth, paralysis, or even death. However, this is not true for ruminant animals such as cattle, goats, and sheep. These aliphatic nitro compounds are degraded in ruminant digestion and do not affect the animals.Crownvetch was originally labeled as a poor forage for farm animals but more recently it has been deemed as a good forage when fed as hay to or grazed by ruminants. It consists of 21.7% crude protein and 22.2% crude fibre. In an experiment involving the digestibility of crownvetch in sheep, it was found that the crude protein is 65.6% and the.

Securigera varia. crude fibre is 46.2% digestible which is similar, but slightly less than the digestibility of alfalfa forage. As previously mentioned, this only applies to ruminant animals as it is toxic to non-ruminants.Crownvetch has been identified as an invasive in several midwestern states. It is very hard to eradicate once established.It is also a common host-plant for the moth "Zygaena ephialtes."BibliographyPurdue University.


Question: What is the height of this building in metre?

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Sighișoara Clock Tower. In every fortification system there is one fortress that dominates the others: the master-tower. The Clock Tower of Sighișoara (, ) is the main entry point to the citadel, opposite guarded by Tailors' Tower. With its 64 meters of height, the tower is visible from almost every corner of the city from Mures County, its purpose was to defend the main gate of the citadel and also served as the town hall until 1556. Now It's considered one of the most expressive clock tower in the whole Transylvania.## History.The tower began to be built at the end of 13th century,.

Sighișoara Clock Tower. to dig for 35m to find a source of water.## Restorations.The tower was modernized in 1964 with an electric motor, without diminishing the archaic effect of the clock. Since 1898, the tower serves as a museum in Sighisoara, a title that gives to it the status of symbol of the Citadel, and the main attraction for visitors.## Architectural Features.The tower is a rectangular prism with massive walls, with a rectangular base measuring 12x8,66 meters, with four floors and an observation gallery. The current distance between the base of the tower and the base of the roof is 30 meters, and.


Question: Who is the discoverer or inventor of this item?

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Tuning fork. A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone once the high overtones fade out. A tuning fork's pitch depends on the length and mass of the two prongs. They are traditional sources of standard pitch for tuning musical instruments.The tuning fork was invented in 1711 by British musician John Shore, Sergeant trumpeter and lutenist.

Tuning fork. John Shore gave to George Frideric Handel produces C=512.Tuning forks, usually C512, are used by medical practitioners to assess a patient's hearing. This is most commonly done with two exams called the Weber test and Rinne test, respectively. Lower-pitched ones, usually at C128, are also used to check vibration sense as part of the examination of the peripheral nervous system.Orthopedic surgeons have explored using a tuning fork (lowest frequency C=128) to assess injuries where bone fracture is suspected. They hold the end of the vibrating fork on the skin above the suspected fracture, progressively closer to the suspected fracture. If.


Question: In which year did this building officially open?

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Lenbachhaus. The Lenbachhaus () is a building housing an art museum in Munich's "Kunstareal".## The building.The Lenbachhaus was built as a Florentine-style villa for the painter Franz von Lenbach between 1887 and 1891 by Gabriel von Seidl and was expanded 1927–1929 by Hans Grässel and again 1969–1972 by Heinrich Volbehr and Rudolf Thönnessen. Some of the rooms have kept their original design.The city of Munich acquired the building in 1924 and opened a museum there in 1929. The latest wing was closed to the public in 2009 to allow the expansion and restoration of the Lenbachhaus by Norman Foster; the 1972.

Lenbachhaus. Objectivity like Christian Schad ("Operation" 1929) and Rudolf Schlichter ("Bertolt Brecht" ) are exhibited in several rooms.## Contemporary art.The museum gives a very profound view of international contemporary art with works by Franz Ackermann, Dennis Adams, Christian Boltanski, Monica Bonvicini, James Coleman, Thomas Demand, Olafur Eliasson, Valie Export, Dan Flavin, Günther Förg, Günter Fruhtrunk, Rupprecht Geiger, Isa Genzken, Liam Gillick, Katharina Grosse, Michael Heizer, Andy Hope 1930 (Andreas Hofer), Jenny Holzer, Stefan Huber, Asger Jorn, Ellsworth Kelly, Anselm Kiefer, Michaela Melian, Gerhard Merz, Maurizio Nannucci, Roman Opałka, Sigmar Polke, Arnulf Rainer, Gerhard Richter, Michael Sailstorfer, Richard Serra, Katharina Sieverding, Andy.

Lenbachhaus. Thayer and C. Spencer Yeh and adding to the collection works by Vito Acconci, Valie Export and Martha Rosler, and worked on a retrospective of Polish-born feminist artist Lea Lublin that opened in summer 2015.On 26 July 2017 a legal battle over a Paul Klee painting titled "Swamp Legend" (1919), seized by Nazis as "degenerate" art in the 1930s, reached a settlement:## Provenance Research.The Lenbachhaus systematically checks the provenance of artworks created before 1945 that entered the collection after 1933. In addition to the examination of the museum's own collection holdings, preliminary reviews of possible new acquisitions, assumptions of permanent.

Lenbachhaus. loans, or endowments also take place. The Lenbachhaus is one of several German museums that are researching the art collector Carl Heumann (1886–1945), who after building in the 1920s and 1930s an important collection of prints of German and Austrian art of the 18th and 19th centuries, was persecuted because of his Jewish origins under the National Socialist regime. The Lenbachhaus approached Carl Heumann's descendants in order to find a just and fair solution regarding the artworks from his collection. Lenbachhaus website Lenbachhaus at the Google Art Project.


Question: What is the source that produces this material?

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Tortoiseshell. Tortoiseshell or tortoise shell is a material produced from the shells of the larger species of tortoise and turtle, mainly the hawksbill sea turtle, which is a critically endangered species according to the IUCN Red List largely because of its exploitation for this trade. The large size, fine color, and unusual form of the hawksbill's scutes make it especially suitable. The distinctive patterning is referred to in names such as the tortoiseshell cat, several breeds of guinea pig, and the common names of several species of the butterfly genera "Nymphalis" and "Aglais", and some other uses.## Uses.Tortoiseshell was widely used.


Question: Where is this plant native to?

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Dacrycarpus dacrydioides. Dacrycarpus dacrydioides, commonly known as kahikatea (from Māori) and white pine, is a coniferous tree endemic to New Zealand. A podocarp, it is New Zealand's tallest tree, gaining heights of 60 m and a life span of 600 years. It was first described botanically by the French botanist Achille Richard in 1832 as "Podocarpus" "dacrydioides", and was given its current binomial name "Dacrycarpus dacrydioides" in 1969 by the American botanist David de Laubenfels. Analysis of DNA has confirmed its evolutionary relationship with other species in the genera "Dacrycarpus" and "Dacrydium".In traditional Māori culture, it is an important source of timber.

Dacrycarpus dacrydioides. structures may also be to protect seeds from drying out. It supports many smaller plants in its own branches, which are called epiphytes; 100 different species have been recorded on one tree alone.## Description.The kahikatea is a coniferous tree reaching a height of 50–65 (m), making it the tallest New Zealand tree, with a trunk 1–2 (m) through. It has a 600 year life span and gains maturity after between 250 and 450 years. Near the base of the tree, the roots are typically buttressed and grooved. The wood itself is odourless and white. The majority of the trunk is.

Dacrycarpus dacrydioides. and grow overlapping one another tightly.As a conifer, the kahikatea has no flowers and instead has cones. Male cones, which occur on different trees to female ones, are 1 cm long and rectangular. The pollen is a pale yellow colour and has a three-pored or trisaccate shape that is distinctive in the New Zealand flora and so can be identified easily. The fruit is highly modified with a yellow-orange fleshy receptacle that is 2.5–6.5 mm long. The purple-black seed is roughly spherical and 4–6 mm in diameter. Both the seed and the ovary are covered with a thin layer of.

Dacrycarpus dacrydioides. wax. The kahikatea has a diploid chromosome count of 20.## Phytochemistry.Several different glycosides have been isolated from the leaves; the tricetin 3’,5’-di-O-/β-glucopyranoside and 3’-0-β-xylopyranoside have been found only in the kahikatea. The receptacles and seeds have been found to contain anthocyanins, rare in gymnosperms, which it was suggested in one 1988 paper make the fruit as a whole more attractive to prospective animal dispersers.## Taxonomy.The kahikatea was first described in 1832 by the French botanist Achille Richard in his "Essai d'une Flore de la Nouvelle Zélande" (Essay On The Flora of New Zealand) as "Podocarpus" "dacrydioides". There is an earlier.

Dacrycarpus dacrydioides. the North, South, and Stewart Islands of New Zealand. It inhabits mostly lowland forests between 0 and 600m above sea level, though may in rare cases reach montane areas. It used to dominate a swamp forest type that now exists almost only on the South Westland region of the South Island. Kahikatea prefers flooded or alluvial soils with low levels of drainage, which in Westland occur from post glaciation events.## Ecology.## Dispersal.Under optimal circumstances a mature kahikatea can produce 800 (kg) of fruit, equivalent to 4.5 million seeds, in a year. The fruit contains a special fleshy structure called a.

Dacrycarpus dacrydioides. receptacle which helps attract birds such as the kererū, tūī, and bellbird, who then eat the fruit and disperse the seed elsewhere. One 2008 study in the New Zealand Journal of Ecology found a mean retention time of kahikatea seeds in kererū of 44.5 minutes. It was suggested in a 1989 study that the high water content of the receptacle may also help protect the seeds, which are vulnerable to drying out, from dry conditions. It may also serve as a storage vessel for water. The bluish seeds have very strong UV reflectance, which is visible to some species of.

Dacrycarpus dacrydioides. newer ones, and also have higher growth rates. Following flooding or other natural events, the kahikatea has been found to require an open canopy in order to re-establish. Because of the consistency of these events in South Westland however, many forested areas don't progress beyond regaining kahikatea and rimu, as other species, such as kāmahi, need the environment to improve before they can return.## Conservation.Prior to the arrival of humans in New Zealand around 75% of the country was covered in trees, and kahikatea dominated its own and once widespread kahikatea forest type. Even after the burning of many forests.

Dacrycarpus dacrydioides. to 600 years old. Reservation of stands may not totally protect kahikatea, however, because the alluvial plains that they favour are prone to upheaval and erosion and so trees may still become damaged. Forest remnants outside of South Westland face the threat of never returning to their natural states, as a result of their small size, threats from weed species, and grazing by livestock. Despite this, the kahikatea has been classified as Least concern by the International Union for Conservation of Nature and "Not Threatened" by the New Zealand Threat Classification System, which gives it an estimated population of above.


Question: What is the vertex figure of this object?

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Octagon. angles total 360°.If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other).The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on the sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite.

Octagon. squares themselves form the vertices of a square.## Regular octagon.A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}.The internal angle at each vertex of a regular octagon is 135° (formula_1 radians). The central angle is 45° (formula_2 radians).## Area.The area of a regular octagon of side length "a" is given byformula_3In terms of the circumradius "R", the area isformula_4In terms of the apothem "r" (see also.