History.

From January into August 1968, under the rule of Communist Party leader Alexander Dubček, Czechoslovakians experienced the Prague Spring. In August, Soviet and other Warsaw Pact troops invaded Czechoslovakia. This led to the overthrow of Dubček and to what came to be known as the normalization process. Less than a month after the invasion, Plastic People of the Universe was formed.  Bassist Milan Hlavsa formed the band in 1968 and was heavily influenced by Frank Zappa and the Velvet Underground (Zappa's band, the Mothers of Invention, had a song called "Plastic People" from their 1967 album "Absolutely Free"). Czech art historian and cultural critic Ivan Jirous became their manager/artistic director in the following year, fulfilling a role similar to the one Andy Warhol had with the Velvet Underground. Jirous introduced Hlavsa to guitarist Josef Janíček, and viola player Jiří Kabeš. The consolidated Czech communist government revoked the band's musicians license in 1970.  Because Ivan Jirous believed that English was the lingua franca of rock music, he invited Paul Wilson, a Canadian who had been teaching in Prague, to teach the band the lyrics of the American songs they covered and to translate their original Czech lyrics into English. Wilson served as lead singer for "the Plastics" from 1970 to 1972, and during this time, the band's repertoire drew heavily on songs by the Velvet Underground and the Fugs. The only two songs sung in Czech in this period were "Na sosnové větvi" and "Růže a mrtví", lyrics of both being written by Czech poet Jiří Kolář. Wilson encouraged them to sing in Czech. After he left, saxophonist Vratislav Brabenec joined the band and they began to draw upon poet Egon Bondy whose work had been banned by the government. In the following three years, Bondy's lyrics nearly completely dominated PPU's music. In December 1974, the band recorded their first "studio" album, "Egon Bondy's Happy Hearts Club Banned" (the title being a play on The Beatles' "Sgt. Pepper's Lonely Hearts Club Band"), which was released in France in 1978.  In 1974, thousands of people traveled from Prague to the town of České Budějovice to visit the Plastics' performance. Stopped by police, they were sent back to Prague, and several students were arrested. The band was forced underground until the Velvet Revolution in 1989. Unable to perform openly, an entire underground cultural movement formed around the band during the 1970s. The sympathizers of the movement were often called "máničky", mainly due to their long hair.  In 1976, the Plastics and other people from the underground scene were arrested and put on trial (after performing at the Third festival of the second culture) by the Communist government to make an example. They were convicted of "organized disturbance of the peace" and sentenced to terms in prison ranging from 8 to 18 months. Paul Wilson was deported even though he had left the band in 1972. Although the band was not associated with politics, the Communist regime's accusations against them ended up with many protests. It was partly in protest of these arrests and prosecution that playwright Václav Havel and others wrote the Charter 77. The Trial of the Plastics became a milestone for opposition against the Communist regime in Czechoslovakia for human rights.  In 1978, the PPU recorded Pašijové hry velikonoční (released in Canada as "The Passion Play" at Paul Wilson's company Boží mlýn). The lyrics were written earlier by Vratislav Brabenec. In 1979, followed Jak bude po smrti, being influenced by a Czech philosopher and writer from the first half of the 20th century, Ladislav Klíma. In 1980, they rehearsed and performed a new record, recorded one year later, Co znamená vésti koně (released in Canada as "Leading Horses"). In 1982, Vratislav Brabenec was forced by the police to leave and emigrate to Canada. After he left, the band released its next record Hovězí porážka (1983) and Půlnoční myš (1986, Midnight Mouse). Czech record label Globus International has collected the original work of the Plastic People as 10 CDs, and released them in various forms several times between 1992 and 2004, with various liner notes and photos, and also as a limited edition box set. They have also released other PPU live and solo albums, and related work such as DG 307.  Despite their clashes with the government, the musicians never considered themselves activists and always claimed that they wanted only to play their music. The band broke up in 1988, with some members forming the group Půlnoc (meaning "midnight" in Czech), which recorded briefly for Arista Records in the USA. At President Havel's suggestion, they reunited in 1997 in honor of the 20th anniversary of Charter 77, and have performed around the world regularly since then.  In 1999, along with Lou Reed, Milan Hlavsa performed at the White House during Václav Havel's state visit.  Milan Hlavsa died in 2001 of lung cancer. The band was not sure whether or not to continue without their frontman and main songwriter. However, after long discussions they decided to continue in honour of Hlavsa's memory. Eva Turnová from the group DG 307 became the band's new bass player.

Post-Hlavsa era.

After Milan Hlavsa's death, the Plastic People began to write new songs. The also performed some of their older albums with several orchestras (such as Agon Orchestra). This was Milan Hlavsa's longtime plan he didn't have the chance to achieve. In 2004 the Plastic People introduced an orchestral version of "The Passion Play". In 2005 and 2011 they performed "Jak bude po smrti". In 2014 they introduced an orchestral version of "Co znamená vésti koně?", alongside the Brno Philharmonic orchestra.  Interest in the band was rekindled in 2006 thanks to a new play, "Rock 'n' Roll" by Tom Stoppard, in which two of their recordings are featured. They are also playing a few songs live in Czech performances in the Czech National Theatre. The play's characters also discuss at length the music of the Plastics and its effects on Czech society. The Plastics performed in London for the first time in January 2007 with Turnová on bass.  In December 2009 the band released a new studio album "Maska za maskou". It was their first studio album since "Líně s tebou spím" (2001) and the first without the songwriting of Milan Hlavsa.

The Plastic People of the Universe (PPU) is a Czech rock band from Prague. It was the foremost representative of Prague's underground culture (1968–1989), which had gone against the grain of Czechoslovakia's Communist regime. Due to their non-conformism, members of the band often suffered serious repercussions such as arrests. The group continues to perform despite the death of its founder, main composer and bassist, Milan "Mejla" Hlavsa in 2001.


Founding and political aims.

Motivated in part by the arrest of members of the psychedelic band Plastic People of the Universe, the text of Charter 77 was prepared in 1976. In December 1976, the first signatures were collected. The charter was published on 6 January 1977, along with the names of the first 242 signatories, which represented various occupations, political viewpoints, and religions. Although Václav Havel, Ludvík Vaculík and Pavel Landovský were detained while trying to bring the charter to the Federal Assembly and the Czechoslovak government, and the original document was confiscated, copies circulated as samizdat and on 7 January were published in several western newspapers (including Le Monde, Frankfurter Allgemeine Zeitung, The Times and The New York Times) and transmitted to Czechoslovakia by Czechoslovak-banned radio broadcasters like Radio Free Europe and Voice of America.  Charter 77 criticized the government for failing to implement human rights provisions of a number of documents it had signed, including the 1960 Constitution of Czechoslovakia, the Final Act of the 1975 Conference on Security and Cooperation in Europe (Basket III of the Helsinki Accords), and 1966 United Nations covenants on political, civil, economic, and cultural rights. The document also described the signatories as a "loose, informal, and open association of people... united by the will to strive individually and collectively for respect for human and civil rights in our country and throughout the world." It emphasized that Charter 77 is not an organization, has no statutes or permanent organs, and "does not form the basis for any oppositional political activity." This final stipulation was a careful effort to stay within the bounds of Czechoslovak law, which made organized opposition illegal.  Many of the organization's activists and members gathered on 29 March 2007 at the Orange Tree Theatre in Richmond, London, to observe the movement's 30th anniversary and to discuss the historical impact their movement generated in modern European politics.

Reaction of the government.

The government's reaction to the appearance of Charter 77 was harsh. The official press described the manifesto as "an anti-state, anti-socialist, and demagogic, abusive piece of writing," and individual signatories were variously described as "traitors and renegades," "a loyal servant and agent of imperialism," "a bankrupt politician," and "an international adventurer." As it was considered to be an illegal document, the full text of Charter 77 was never published in the official press. However an official group of artists and writers was mobilized into an "anti-charter" movement which included Czechoslovakia's foremost singer Karel Gott as well as prominent comedic writer Jan Werich who later claimed he had no idea of what he was doing whilst signing the anti-charter.  Several means of retaliation were used against the signatories, including dismissal from work, denial of educational opportunities for their children, suspension of drivers' licenses, forced exile, loss of citizenship, and detention, trial, and imprisonment. Many members were forced to collaborate with the communist secret service (the StB, Czech: Státní bezpečnost).  The treatment of Charter 77 signatories prompted the creation in April 1978 of a support group, the Committee for the Defense of the Unjustly Prosecuted ("Výbor na obranu nespravedlivě stíhaných" – VONS), to publicize the fate of those associated with the charter. In October 1979 six leaders of this support group, including Václav Havel, were tried for subversion and sentenced to prison terms of up to five years.  Repression of Charter 77 and VONS members continued during the 1980s. Despite unrelenting harassment and arrests, however, the groups continued to issue reports on the government's violations of human rights. Until the Velvet Revolution, Charter 77 had approximately 1,900 signatories.

Influence.

Under the dictatorship, the influence of Charter 77 remained limited and only 1,065 people ever signed the document. It didn't reach wide groups of people and most of its members were from Prague. The majority of Czechoslovak citizens knew of the organization only because of the government's campaign against it.  In the late 1980s, as the Eastern Bloc regimes weakened, members of Charter 77 saw their opportunity and became more involved in organizing opposition against the regime in power. During the days of the Velvet Revolution, members of the group negotiated the smooth transfer of political power from dictatorship to democracy. Many were elevated into high positions in the government (e.g. Václav Havel became the President of Czechoslovakia) but since most had no experience in active politics (such as skills in diplomacy or knowledge of capitalism) they met with mixed success.  Charter 77 included people who had a wide range of opinions and, after reaching their common goal, the group's presence faded. An attempt to make the group the focal point of an all-encompassing political party (the Civic Forum) failed and in 1992 the organization was officially dissolved.

Award.

In 1984 Charter 77 was awarded the first Andrei Sakharov Freedom Award.

External links.

Text of the Charter  Further reading

Charter 77 ("Charta 77" in Czech and in Slovak) was an informal civic initiative in the Czechoslovak Socialist Republic from 1976 to 1992, named after the document Charter 77 from January 1977. Founding members and architects were Jiří Němec, Václav Benda, Ladislav Hejdánek, Václav Havel, Jan Patočka, Zdeněk Mlynář, Jiří Hájek, Martin Palouš, Pavel Kohout and Ladislav Lis. Spreading the text of the document was considered a political crime by the communist regime. After the 1989 Velvet Revolution, many of its members played important roles in Czech and Slovak politics.


Chemical structure.

Triglycerides are tri-esters consisting of a glycerol bound to three fatty acid molecules. Alcohols have a hydroxyl (HO–) group. Organic acids have a carboxyl (–COOH) group. Alcohols and organic acids join to form esters. The glycerol molecule has three hydroxyl (HO–) groups and each fatty acid has a carboxyl group (–COOH). In triglycerides, the hydroxyl groups of the glycerol join the carboxyl groups of the fatty acid to form ester bonds:  The three fatty acids (RCOH, R′COH, R′′COH in the above equation) are usually different, as many kinds of triglycerides are known. The chain lengths of the fatty acids in naturally occurring triglycerides vary, but most contain 16, 18, or 20 carbon atoms. Natural fatty acids found in plants and animals are typically composed of only even numbers of carbon atoms, reflecting the pathway for their biosynthesis from the two-carbon building-block acetyl CoA. Bacteria, however, possess the ability to synthesise odd- and branched-chain fatty acids. As a result, ruminant animal fat contains odd-numbered fatty acids, such as 15, due to the action of bacteria in the rumen. Many fatty acids are unsaturated; some are polyunsaturated (e.g., those derived from linoleic acid).  Most natural fats contain a complex mixture of individual triglycerides. Because of this, they melt over a broad range of temperatures. Cocoa butter is unusual in that it is composed of only a few triglycerides, derived from palmitic, oleic, and stearic acids in the 1-, 2-, and 3-positions of glycerol, respectively.

Homotriglycerides.

The simplest triglycerides are those where the three fatty acids are identical. Their names indicate the fatty acid: stearin derived from stearic acid, palmitin derived from palmitic acid, etc. These compounds can be obtained in three crystalline forms (polymorphs): α, β, and β′, the three forms differing in their melting points.

Chirality.

If the first and third chain R and R′′ are different, then the central carbon atom is a chiral center, and as a result the triglyceride is chiral.

Metabolism.

The pancreatic lipase acts at the ester bond, hydrolyzing the bond and "releasing" the fatty acid. In triglyceride form, lipids cannot be absorbed by the duodenum. Fatty acids, monoglycerides (one glycerol, one fatty acid), and some diglycerides are absorbed by the duodenum, once the triglycerides have been broken down.  In the intestine, following the secretion of lipases and bile, triglycerides are split into monoacylglycerol and free fatty acids in a process called lipolysis. They are subsequently moved to absorptive enterocyte cells lining the intestines. The triglycerides are rebuilt in the enterocytes from their fragments and packaged together with cholesterol and proteins to form chylomicrons. These are excreted from the cells and collected by the lymph system and transported to the large vessels near the heart before being mixed into the blood. Various tissues can capture the chylomicrons, releasing the triglycerides to be used as a source of energy. Liver cells can synthesize and store triglycerides. When the body requires fatty acids as an energy source, the hormone glucagon signals the breakdown of the triglycerides by hormone-sensitive lipase to release free fatty acids. As the brain cannot utilize fatty acids as an energy source (unless converted to a ketone), the glycerol component of triglycerides can be converted into glucose, via gluconeogenesis by conversion into dihydroxyacetone phosphate and then into glyceraldehyde 3-phosphate, for brain fuel when it is broken down. Fat cells may also be broken down for that reason if the brain's needs ever outweigh the body's.  Triglycerides cannot pass through cell membranes freely. Special enzymes on the walls of blood vessels called lipoprotein lipases must break down triglycerides into free fatty acids and glycerol. Fatty acids can then be taken up by cells via the fatty acid transporter (FAT).  Triglycerides, as major components of very-low-density lipoprotein (VLDL) and chylomicrons, play an important role in metabolism as energy sources and transporters of dietary fat. They contain more than twice as much energy (approximately 9kcal/g or 38kJ/g) as carbohydrates (approximately 4kcal/g or 17kJ/g).

Role in disease.

In the human body, high levels of triglycerides in the bloodstream have been linked to atherosclerosis, heart disease and stroke. However, the relative negative impact of raised levels of triglycerides compared to that of LDL:HDL ratios is as yet unknown. The risk can be partly accounted for by a strong inverse relationship between triglyceride level and HDL-cholesterol level. But the risk is also due to high triglyceride levels increasing the quantity of small, dense LDL particles.

Guidelines.

The National Cholesterol Education Program has set guidelines for triglyceride levels: These levels are tested after fasting 8 to 12 hours. Triglyceride levels remain temporarily higher for a period after eating.  The American Heart Association recommends an optimal triglyceride level of 100mg/dL (1.1mmol/L) or lower to improve heart health.

Reducing triglyceride levels.

Weight loss and dietary modification are effective first-line lifestyle modification treatments for hypertriglyceridemia. For people with mildly or moderately high levels of triglycerides, lifestyle changes, including weight loss, moderate exercise and dietary modification, are recommended. This may include restriction of carbohydrates (specifically fructose) and fat in the diet and the consumption of omega-3 fatty acids from algae, nuts, and seeds. Medications are recommended in those with high levels of triglycerides that are not corrected with the aforementioned lifestyle modifications, with fibrates being recommended first. Omega-3-carboxylic acids is another prescription drug used to treat very high levels of blood triglycerides.  The decision to treat hypertriglyceridemia with medication depends on the levels and on the presence of other risk factors for cardiovascular disease. Very high levels that would increase the risk of pancreatitis is treated with a drug from the fibrate class. Niacin and omega-3 fatty acids as well as drugs from the statin class may be used in conjunction, with statins being the main medication for moderate hypertriglyceridemia when reduction of cardiovascular risk is required.

Industrial uses.

Linseed oil and related oils are important components of useful products used in oil paints and related coatings. Linseed oil is rich in di- and tri-unsaturated fatty acid components, which tend to harden in the presence of oxygen. This heat-producing hardening process is peculiar to these so-called "drying oils". It is caused by a polymerization process that begins with oxygen molecules attacking the carbon backbone.  Triglycerides are also split into their components via transesterification during the manufacture of biodiesel. The resulting fatty acid esters can be used as fuel in diesel engines. The glycerin has many uses, such as in the manufacture of food and in the production of pharmaceuticals.

Staining.

Staining for fatty acids, triglycerides, lipoproteins, and other lipids is done through the use of lysochromes (fat-soluble dyes). These dyes can allow the qualification of a certain fat of interest by staining the material a specific color. Some examples: Sudan IV, Oil Red O, and Sudan Black B.

A triglyceride (TG, triacylglycerol, TAG, or triacylglyceride) is an ester derived from glycerol and three fatty acids (from "tri-" and "glyceride"). Triglycerides are the main constituents of body fat in humans and other vertebrates, as well as vegetable fat. They are also present in the blood to enable the bidirectional transference of adipose fat and blood glucose from the liver, and are a major component of human skin oils.


Life.

Gris was born in Madrid and later studied engineering at the Madrid School of Arts and Sciences. There, from 1902 to 1904, he contributed drawings to local periodicals. From 1904 to 1905, he studied painting with the academic artist José Moreno Carbonero. It was in 1905 that José Victoriano González adopted the more distinctive name Juan Gris.  In 1909 Lucie Belin (1891–1942)—Gris' wife—gave birth to Georges Gonzalez-Gris (1909–2003), the artist's only child. The three lived at the Bateau-Lavoir, 13 Rue Ravignan, Paris, from 1909 to 1911. In 1912 Gris met Charlotte Augusta Fernande Herpin (1894–1983), also known as Josette. Late 1913 or early 1914 they lived together at the Bateau-Lavoir until 1922. Josette Gris was Juan Gris' second companion and unofficial wife.

Career.

In 1906 he moved to Paris and became friends with the poets Guillaume Apollinaire, Max Jacob, and artists Henri Matisse, Georges Braque, Fernand Léger and Jean Metzinger. He submitted darkly humorous illustrations to journals such as the anarchist satirical magazine "L'Assiette au Beurre", and also "Le Rire", "Le Charivari", and "Le Cri de Paris". In Paris, Gris followed the lead of Metzinger and another friend and fellow countryman, Pablo Picasso.  Gris began to paint seriously in 1911 (when he gave up working as a satirical cartoonist), developing at this time a personal Cubist style. In "A Life of Picasso", John Richardson writes that Jean Metzinger's 1911 work, "Le goûter (Tea Time)", persuaded Juan Gris of the importance of mathematics in painting. Gris exhibited for the first time at the 1912 Salon des Indépendants (a painting entitled "Hommage à Pablo Picasso").  "He appears with two styles", writes art historian Peter Brooke, "In one of them a grid structure appears that is clearly reminiscent of the "Goûter" and of Metzinger's later work in 1912." In the other, Brooke continues, "the grid is still present but the lines are not stated and their continuity is broken. Their presence is suggested by the heavy, often triangular, shading of the angles between them... Both styles are distinguished from the work of Picasso and Braque by their clear, rational and measurable quality." Although Gris regarded Picasso as a teacher, Gertrude Stein wrote in "The Autobiography of Alice B. Toklas" that "Juan Gris was the only person whom Picasso wished away". In 1912 Gris exhibited at the "Exposicío d'art cubista", Galeries Dalmau in Barcelona, the first declared group exhibition of Cubism worldwide; the gallery Der Sturm in Berlin; the "Salon de la Société Normande de Peinture Moderne" in Rouen; and the Salon de la Section d'Or in Paris. Gris, in that same year, signed a contract that gave Daniel-Henry Kahnweiler exclusive rights to his work.  At first Gris painted in the style of "Analytical Cubism", a term he himself later coined, but after 1913 he began his conversion to "Synthetic Cubism", of which he became a steadfast interpreter, with extensive use of papier collé or, collage. Unlike Picasso and Braque, whose Cubist works were practically monochromatic, Gris painted with bright harmonious colors in daring, novel combinations in the manner of his friend Matisse. Gris exhibited with the painters of the Puteaux Group in the Salon de "la Section d'Or" in 1912. His preference for clarity and order influenced the Purist style of Amédée Ozenfant and Charles Edouard Jeanneret (Le Corbusier), and made Gris an important exemplar of the post-war "return to order" movement. In 1915 he was painted by his friend, Amedeo Modigliani. In November 1917 he made one of his few sculptures, the polychrome plaster "Harlequin".

Crystal Cubism.

Gris's works from late 1916 through 1917 exhibit a greater simplification of geometric structure, a blurring of the distinction between objects and setting, between subject matter and background. The oblique overlapping planar constructions, tending away from equilibrium, can best be seen in "Woman with Mandolin, after Corot" (September 1916) and in its epilogue, "Portrait of Josette Gris" (October 1916; Museo Reina Sofia).  The clear-cut underlying geometric framework of these works seemingly controls the finer elements of the compositions; the constituent components, including the small planes of the faces, become part of the unified whole. Though Gris certainly had planned the representation of his chosen subject matter, the abstract armature serves as the starting point.  The geometric structure of Juan Gris's Crystal period is already palpable in "Still Life before an Open Window, Place Ravignan" (June 1915; Philadelphia Museum of Art). The overlapping elemental planar structure of the composition serves as a foundation to flatten the individual elements onto a unifying surface, foretelling the shape of things to come.  In 1919 and particularly 1920, artists and critics began to write conspicuously about this'synthetic' approach, and to assert its importance in the overall scheme of advanced Cubism.

Designer and theorist.

In 1924, he designed ballet sets and costumes for Sergei Diaghilev and the famous Ballets Russes.  Gris articulated most of his aesthetic theories during 1924 and 1925. He delivered his definitive lecture, "Des possibilités de la peinture", at the Sorbonne in 1924. Major Gris exhibitions took place at the Galerie Simon in Paris and the Galerie Flechtheim in Berlin in 1923 and at the Galerie Flechtheim in Düsseldorf in 1925.

Death.

After October 1925, Gris was frequently ill with bouts of uremia and cardiac problems. He died of kidney failure in Boulogne-sur-Seine (Paris) on 11 May 1927, at the age of 40, leaving a wife, Josette, and a son, Georges.

Art market.

The top auction price for a Gris work is $57.1 million (£34.8 million), achieved for his 1915 painting "Nature morte à la nappe à carreaux (Still Life with Checked Tablecloth)". This surpassed previous records of $20.8 million for his 1915 still life "Livre, pipe et verres", $28.6 million for the 1913 artwork "Violon et guitare" and $31.8 million for "The musician's table", now in the Met.

José Victoriano (Carmelo Carlos) González-Pérez (23 March 1887 – 11 May 1927), better known as Juan Gris (; ), was a Spanish painter born in Madrid who lived and worked in France most of his life. Closely connected to the innovative artistic genre Cubism, his works are among the movement's most distinctive.


Morphology.

"Aldrovanda vesiculosa" is a rootless aquatic plant. Seedlings develop a short protoroot; however, this fails to develop further and senesces. The plant consists of floating stems reaching a length of. The trap leaves grow in whorls of between 5 and 9 in close succession along the plant's central stem. The actual traps are held by petioles which hold air sacs that aid in flotation. One end of the stem continually grows while the other end dies off. Growth is quite rapid ( per day in Japanese populations), so that in optimal conditions a new whorl is produced once or more each day.

Trap.

The actual traps consist of two lobes which fold together to form a snap-trap similar to that of the Venus fly trap, except that it is smaller and located underwater. These traps, which are twisted so that the trap openings point outward, are lined on the inside by a fine coating of trigger hairs, snapping shut in response to contact with aquatic invertebrates and trapping them. The closing of this trap takes 10–20 milliseconds, making it one of the fastest examples of plant movement in the kingdom. This trapping is only possible in warm conditions of at least. Each trap is surrounded by between four and six 6–8 mm long bristles that prevent triggering of traps by debris in the water.

Reproduction.

Flowers.

The small, solitary white flowers of "A. vesiculosa" are supported above the water level by short peduncles which arise from whorl axes. The flower only opens for a few hours, after which the structure is brought back beneath the water level for seed production. The seeds are cryptocotylar: the cotyledons remain hidden within the seed coat and serve as energy storage for the seedlings. Flowering, however, is rare in temperate regions and poorly successful in terms of fruit and seed development.

Divisions.

"Aldrovanda vesiculosa" reproduces most often through vegetative reproduction. In favourable conditions, adult plants will produce an offshoot every, resulting in new plants as the tips continue to grow and the old ends die off and separate. Due to the rapid growth rate of this species, countless new plants can be produced in a short period of time in this fashion.

Turions.

Winter-hardy "Aldrovanda" form turions as a frost survival strategy. At the onset of winter, the growth tip starts producing highly reduced non-carnivorous leaves on a severely shortened stem. This results in a tight bud of protective leaves which, being heavier and having released flotational gases, breaks off the mother plant and sinks to the water bottom, where temperatures are stable and warmer. Here it can withstand temperatures as low as. In the wild, "Aldrovanda" turions have been observed to have a relatively low rate of successful sinking. Those nutritious turions that fail to sink are then grazed by waterfowl or are killed by the onset of frost. In spring when water temperatures rise above, turions reduce their density and float to the top of the water, where they germinate and resume growth. Non-dormant turion-like organs can also form in response to summer drought.

Distribution.

"Aldrovanda vesiculosa" is the most widely distributed carnivorous plant species, native to Europe, Asia, Africa, and Australia. "Aldrovanda" is spread mainly through the movement of waterfowl: plants sticking to the feet of a bird are transported to the next aquatic destination on the bird's route. As a result, most "Aldrovanda" populations are located along avian migratory routes. Throughout the last century the species has become increasingly rare, listed as extinct in an increasingly large number of countries.

Habitat.

"A. vesiculosa" prefers clean, shallow, warm, standing water with bright light, low nutrient levels, and a slightly acidic pH (around 6). It can be found floating amongst Juncus, reeds, and even rice.

Botanical history.

"Aldrovanda vesiculosa" was first mentioned in 1696 by Leonard Plukenet, based on collections made in India. He named the plant "Lenticula pulustris Indica". The modern botanical name originates from Gaetano Lorenzo Monti, who described Italian specimens in 1747 and named them "Aldrovandia vesiculosa" in honor of the Italian naturalist Ulisse Aldrovandi. When Carl Linnaeus published his "Species Plantarum" in 1753, the "i" was dropped from the name (an apparent orthographic error) to form the modern binomial.

Aldrovanda vesiculosa, commonly known as the waterwheel plant, is the sole extant species in the flowering plant genus "Aldrovanda" of the family Droseraceae. The plant captures small aquatic invertebrates using traps similar to those of the Venus flytrap. The traps are arranged in whorls around a central, free-floating stem, giving rise to the common name. This is one of the few plant species capable of rapid movement.


History.

Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by which some of these numbers could be derived was invented circa 850 by the Iraqi mathematician Thābit ibn Qurra (826–901). Other Arab mathematicians who studied amicable numbers are al-Majriti (died 1007), al-Baghdadi (980–1037), and al-Fārisī (1260–1320). The Iranian mathematician Muhammad Baqir Yazdi (16th century) discovered the pair (9363584, 9437056), though this has often been attributed to Descartes. Much of the work of Eastern mathematicians in this area has been forgotten.  Thābit ibn Qurra's formula was rediscovered by Fermat (1601–1665) and Descartes (1596–1650), to whom it is sometimes ascribed, and extended by Euler (1707–1783). It was extended further by Borho in 1972. Fermat and Descartes also rediscovered pairs of amicable numbers known to Arab mathematicians. Euler also discovered dozens of new pairs. The second smallest pair, (1184, 1210), was discovered in 1866 by a then teenage B. Nicolò I. Paganini (not to be confused with the composer and violinist), having been overlooked by earlier mathematicians.  By 1946 there were 390 known pairs, but the advent of computers has allowed the discovery of many thousands since then. Exhaustive searches have been carried out to find all pairs less than a given bound, this bound being extended from 10 in 1970, to 10 in 1986, 10 in 1993, 10 in 2015, and to 10 in 2016. , there are over 1,225,063,681 known amicable pairs.

Rules for generation.

While these rules do generate some pairs of amicable numbers, many other pairs are known, so these rules are by no means comprehensive.  In particular, the two rules below produce only even amicable pairs, so they are of no interest for the open problem of finding amicable pairs coprime to 210 = 2·3·5·7, while over 1000 pairs coprime to 30 = 2·3·5 are known [García, Pedersen & te Riele (2003), Sándor & Crstici (2004)].

Thābit ibn Qurra theorem.

The Thābit ibn Qurra theorem is a method for discovering amicable numbers invented in the ninth century by the Arab mathematician Thābit ibn Qurra.  It states that if where is an integer and,, and are prime numbers, then and are a pair of amicable numbers. This formula gives the pairs for, for, and for, but no other such pairs are known. Numbers of the form are known as Thabit numbers. In order for Ibn Qurra's formula to produce an amicable pair, two consecutive Thabit numbers must be prime; this severely restricts the possible values of.  To establish the theorem, Thâbit ibn Qurra proved nine lemmas divided into two groups. The first three lemmas deal with the determination of the aliquot parts of a natural integer. The second group of lemmas deals more specifically with the formation of perfect, abundant and deficient numbers.

Euler's rule.

"Euler's rule" is a generalization of the Thâbit ibn Qurra theorem. It states that if where are integers and,, and are prime numbers, then and are a pair of amicable numbers. Thābit ibn Qurra's theorem corresponds to the case. Euler's rule creates additional amicable pairs for with no others being known. Euler (1747 & 1750) overall found 58 new pairs to make all the by then existing pairs into 61.

Regular pairs.

Let (, ) be a pair of amicable numbers with, and write and where is the greatest common divisor of and. If and are both coprime to and square free then the pair (, ) is said to be regular, otherwise it is called irregular or exotic. If (, ) is regular and and have and prime factors respectively, then is said to be of type.  For example, with, the greatest common divisor is and so and. Therefore, is regular of type.

Twin amicable pairs.

An amicable pair is twin if there are no integers between and belonging to any other amicable pair.

Other results.

In every known case, the numbers of a pair are either both even or both odd. It is not known whether an even-odd pair of amicable numbers exists, but if it does, the even number must either be a square number or twice one, and the odd number must be a square number. However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10. Also, a pair of coprime amicable numbers cannot be generated by Thabit's formula (above), nor by any similar formula.  In 1955, Paul Erdős showed that the density of amicable numbers, relative to the positive integers, was 0.  According to the sum of amicable pairs conjecture, as the number of the amicable numbers approaches infinity, the percentage of the sums of the amicable pairs divisible by ten approaches 100%.

Generalizations.

Amicable tuples.

Amicable numbers formula_1 satisfy formula_2 and formula_3 which can be written together as formula_4. This can be generalized to larger tuples, say formula_5, where we require  For example, (1980, 2016, 2556) is an amicable triple, and (3270960, 3361680, 3461040, 3834000) is an amicable quadruple.  Amicable multisets are defined analogously and generalizes this a bit further.

Sociable numbers.

Sociable numbers are the numbers in cyclic lists of numbers (with a length greater than 2) where each number is the sum of the proper divisors of the preceding number. For example, formula_7 are sociable numbers of order 4.

Searching for sociable numbers.

The aliquot sequence can be represented as a directed graph, formula_8, for a given integer formula_9, where formula_10 denotes the sum of the proper divisors of formula_11. Cycles in formula_8 represent sociable numbers within the interval formula_13. Two special cases are loops that represent perfect numbers and cycles of length two that represent amicable pairs.

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.


Early life and studies.

Ørsted was born in Rudkøbing in 1777. As a young boy he developed an interest in science while working for his father, who owned the local pharmacy. He and his brother Anders received most of their early education through self-study at home, going to Copenhagen in 1793 to take entrance exams for the University of Copenhagen, where both brothers excelled academically. By 1796, Ørsted had been awarded honors for his papers in both aesthetics and physics. He earned his doctorate in 1799 for a dissertation based on the works of Kant entitled "The Architectonics of Natural Metaphysics".  In 1800, Alessandro Volta reported his invention of the voltaic pile, which inspired Ørsted to investigate the nature of electricity and to conduct his first electrical experiments. In 1801, Ørsted received a travel scholarship and public grant which enabled him to spend three years traveling across Europe. He toured science headquarters throughout the continent, including in Berlin and Paris.  In Germany Ørsted met Johann Wilhelm Ritter, a physicist who believed there was a connection between electricity and magnetism. This idea made sense to Ørsted as he subscribed to Kantian thought regarding the unity of nature. Ørsted's conversations with Ritter drew him into the study of physics. He became a professor at the University of Copenhagen in 1806 and continued research on electric currents and acoustics. Under his guidance the university developed a comprehensive physics and chemistry program and established new laboratories.  Ørsted welcomed William Christopher Zeise to his family home in autumn 1806. He granted Zeise a position as his lecturing assistant and took the young chemist under his tutelage. In 1812, Ørsted again visited Germany and France after publishing "Videnskaben om Naturens Almindelige Love" and "Første Indledning til den Almindelige Naturlære" (1811).  Ørsted was the first modern thinker to explicitly describe and name the thought experiment. He used the Latin-German term "Gedankenexperiment" circa 1812 and the German term "Gedankenversuch" in 1820.

Electromagnetism.

On 21 April 1820, Ørsted published his discovery that a compass needle was deflected from magnetic north by a nearby electric current, confirming a direct relationship between electricity and magnetism. The often reported story that Ørsted made this discovery incidentally during a lecture is a myth. He had, in fact, been looking for a connection between electricity and magnetism since 1818, but was quite confused by the results he was obtaining.  His initial interpretation was that magnetic effects radiate from all sides of a wire carrying an electric current, as do light and heat. Three months later, he began more intensive investigations and soon thereafter published his findings, showing that an electric current produces a circular magnetic field as it flows through a wire. For his discovery, the Royal Society of London awarded Ørsted the Copley Medal in 1820 and the French Academy granted him 3,000 francs.  Ørsted's findings stirred much research into electrodynamics throughout the scientific community, influencing French physicist André-Marie Ampère's developments of a single mathematical formula to represent the magnetic forces between current-carrying conductors. Ørsted's work also represented a major step toward a unified concept of energy.

Later years.

Ørsted was elected a foreign member of the Royal Swedish Academy of Sciences in 1822 and a Foreign Honorary Member of the American Academy of Arts and Sciences in 1849.  He founded Selskabet for Naturlærens Udbredelse (SNU), a society to disseminate knowledge of the natural sciences, in 1824. He was also the founder of predecessor organizations which eventually became the Danish Meteorological Institute and the Danish Patent and Trademark Office. In 1829, Ørsted founded Den Polytekniske Læreanstalt ('College of Advanced Technology') which was later renamed the Technical University of Denmark (DTU).  In 1825, Ørsted made a significant contribution to chemistry by producing aluminium in a near-pure form for the first time. In 1808, Humphry Davy had predicted the existence of the metal which he gave the name of alumium. However his attempts to isolate it using electrolysis processes were unsuccessful. The closest he came was an aluminum-iron alloy. Ørsted was the first to isolate the element via a reduction of aluminium chloride. Although the aluminium alloy he extracted still contained impurities, he is credited with discovery of the metal. His work was developed further by Friedrich Wöhler who obtained aluminium powder on October 22, 1827, and solidified balls of molten aluminium in 1845. Wöhler is credited with the first isolation of the metal in a pure form.  Ørsted died in Copenhagen in 1851, aged 73, and was buried in the Assistens Cemetery.

Legacy.

The centimetre-gram-second system (CGS) unit of magnetic induction (oersted) is named for his contributions to the field of electromagnetism.

Toponomy.

The Ørsted Park in Copenhagen was named after Ørsted in 1879. The streets H.C. Ørsteds Vej in Frederiksberg and H. C. Ørsteds Allé in Galten are also named after him.  The buildings that are home to the Department of Chemistry and the Institute for Mathematical Sciences at the University of Copenhagen's North Campus are named the "H.C. Ørsted Institute", after him. A dormitory named H. C. Ørsted Kollegiet is located in Odense.  The first Danish satellite, launched 1999, was named after Ørsted.

Monuments and memorials.

A statue of Hans Christian Ørsted was installed in the Ørsted Park in 1880. A commemorative plaque is located above the gate on the building in Studiestræde where he lived and worked. The 100 danske kroner note issued from 1950 to 1970 carried an engraving of Ørsted.

Awards and lectures.

Two medals are awarded in Ørsted's name: the Oersted Medal for notable contributions in the teaching of physics in America, awarded by American Association of Physics Teachers, along with the H. C. Ørsted Medal for Danish scientists, awarded by the Danish "Selskabet for Naturlærens Udbredelse" (Society for the Dissemination of Natural Science), founded by Ørsted.  The H.C. Ørsted Lectureship is awarded to two prominent researchers annually.  Here is a list of some of the previous H.C. Ørsted lecturers:

Writings.

Ørsted was a published writer and poet. His poetry series "Luftskibet" ("The Airship") was inspired by the balloon flights of fellow physicist and stage magician Étienne-Gaspard Robert. Shortly before his death, he submitted a collection of articles for publication under the title "The Soul in Nature". The book presents Ørsted's life philosophy and views on a wide variety of issues.

Hans Christian Ørsted (, ; often rendered Oersted in English; 14 August 17779 March 1851) was a Danish physicist and chemist who discovered that electric currents create magnetic fields, which was the first connection found between electricity and magnetism. Oersted's law and the oersted (Oe) are named after him.


Childhood.

Christiaan Karel Appel was born on 25 April 1921 in his parents' house at Dapperstraat 7 in Amsterdam, the Netherlands. As a child he was often called 'Kik'. On the ground floor his father, Jan Appel, had a barbershop. His mother, born Johanna Chevalier, was a descendant of French Huguenots. Karel Appel had three brothers.  At fourteen, Appel produced his first real painting on canvas, a still life of a fruit basket. For his fifteenth birthday, his wealthy uncle Karel Chevalier gave him a paint set and an easel. An avid amateur painter himself, Chevalier gave his namesake some lessons in painting.

Career.

From 1940 to 1943, during the German occupation, Appel studied at the Rijksakademie van Beeldende Kunsten in Amsterdam, and it was there he met the young painter Corneille and, some years later, Constant; they became close friends for years. His parents opposed his choice to become an artist, leading him to leave home; this was also necessary because he needed to hide from the German police so that he would not be picked up and sent to Germany to work in the weapons industry. Appel had his first show in Groningen in 1946. In 1949 he participated with the other CoBrA artists in the Stedelijk Museum Amsterdam; this generated a huge scandal and many objections in the press and public. He was influenced by Pablo Picasso, Henri Matisse, and the French brute-art artist Jean Dubuffet. In 1947 he started sculpting with all kinds of used materials (in the technique of assemblage) and painted them in bright colors: white, red, yellow, blue, and black. He joined the Experimentele Groep in Holland together with the young Dutch painters Anton Rooskens, Theo Wolvecamp, and Jan Nieuwenhuys. Later the Belgian writer Hugo Claus joined the group.  In 1948 Appel joined CoBrA (from Copenhagen, Brussels, Amsterdam) together with the Dutch artists Corneille, Constant, and Jan Nieuwenhuys (see also Aart Kemink), and with the Belgian poet Christian Dotremont. The new art of the CoBrA group was not popular in the Netherlands, but it found a warm and broad welcome in Denmark. By 1939, Danish artists had already started to make spontaneous art and one of their sources of inspiration was Danish and Nordic mythology. It was also in Denmark that the CoBrA artists started cooperating by collectively painting the insides of houses, which encouraged and intensified the exchange of the typical 'childish' and spontaneous picture language used by the CoBrA group. Appel used this very intensively; his 1949 fresco 'Questioning Children' in Amsterdam City Hall caused controversy and was covered up for ten years.  As a result of this controversy and other negative Dutch reactions to CoBrA, Appel moved to Paris in 1950 and developed his international reputation by travelling to Mexico, the USA, Yugoslavia, and Brazil. He also lived in New York City and Florence. His first American gallery exhibition took place in 1954 at the Martha Jackson Gallery. The following year his painting "Child and Beast II" (1951) was included in the influential exhibition, "The New Decade" at the Museum of Modern Art which featured the work of twenty-two European painters and sculptors including newcomers like Francis Bacon, Jean Dubuffet, and Pierre Soulages. He is particularly noted for his mural work. After 1990 he became much more popular in the Netherlands; he had several big shows in Amsterdam and Bruxelles, organized by director Rudy Fuchs. Also, the CoBrA-museum in Amstelveen organized several shows featuring his work. He became the most famous Dutch CoBrA artist. Appel's work has been exhibited in a number of galleries, including the Anita Shapolsky Gallery in New York City, Galerie Lelong in Paris, Galerie Ulysses in Vienna, and Gallery LL in Amsterdam.

Death.

Appel died on 3 May 2006 in his home in Zürich, Switzerland. He suffered from a heart ailment. He was buried on 16 May 2006 at the Père Lachaise Cemetery in Paris, France.  Years before his death, Appel established the Karel Appel Foundation, whose purpose is "to preserve [Appel's] artworks, to promote public awareness and knowledge of Karel Appel's oeuvre, and to supervise publication of the Oeuvre Catalogue of the paintings, the works on paper, and the sculptures."  In 2002 a number of Appel's works went missing on the way to his foundation, an event that was not to be resolved before his death. However, in 2012 the works were found in a disused UK warehouse and returned to the foundation.  In the wake of his death, the Foundation (based in Amsterdam) functions as his official estate in addition to its primary service as an image archive. The U.S. copyright representative for the Karel Appel Foundation is the Artists Rights Society.

Public collections.

Among the public collections holding works by Karel Appel are:

Christiaan Karel Appel (; 25 April 1921 – 3 May 2006) was a Dutch painter, sculptor, and poet. He started painting at the age of fourteen and studied at the Rijksakademie in Amsterdam in the 1940s. He was one of the founders of the avant-garde movement Cobra in 1948. He was also an avid sculptor and has had works featured in MoMA and other museums worldwide.


Function and types.

The traditional function of a signature is to permanently affix to a document a person's uniquely personal, undeniable self-identification as physical evidence of that person's personal witness and certification of the content of all, or a specified part, of the document. For example, the role of a signature in many consumer contracts is not solely to provide evidence of the identity of the contracting party, but also to provide evidence of deliberation and informed consent. In many countries, signatures may be witnessed and recorded in the presence of a notary public to carry additional legal force. On legal documents, an illiterate signatory can make a "mark" (often an "X" but occasionally a personalized symbol), so long as the document is countersigned by a literate witness. In some countries, illiterate people place a thumbprint on legal documents in lieu of a written signature.  In the United States, signatures encompass marks and actions of all sorts that are indicative of identity and intent. The legal rule is that unless a statute specifically prescribes a particular method of making a signature it may be made in any number of ways. These include by a mechanical or rubber stamp facsimile. A signature may be made by the purported signatory; alternatively someone else duly authorized by the signatory, acting in the signer's presence and at the signatory's direction, may make the signature.  Many individuals have much more fanciful signatures than their normal cursive writing, including elaborate ascenders, descenders and exotic flourishes, much as one would find in calligraphic writing. As an example, the final "k" in John Hancock's famous signature on the US Declaration of Independence loops back to underline his name. This kind of flourish is also known as a "paraph".  Paraphe is a term meaning flourish, initial or signature in French. The paraph is used in graphology analyses.  Several cultures whose languages use writing systems other than alphabets do not share the Western notion of signatures per se: the "signing" of one's name results in a written product no different from the result of "writing" one's name in the standard way. For these languages, to write or to sign involves the same written characters. Also see Calligraphy.

Mechanically produced signatures.

Special signature machines, called autopens, are capable of automatically reproducing an individual's signature. These are typically used by people required to sign a lot of printed matter, such as celebrities, heads of state or CEOs. More recently, Members of Congress in the United States have begun having their signature made into a TrueType font file. This allows staff members in the Congressman's office to easily reproduce it on correspondence, legislation, and official documents. In the East Asian languages of Chinese, Japanese, and Korean, people traditionally use stamp-like objects known as "name-seals" with the name carved in "tensho" script ("seal script") in lieu of a handwritten signature.

Wet signatures.

Some government agencies require that professional persons or official reviewers sign originals and all copies of originals to authenticate that they personally viewed the content. In the United States this is prevalent with architectural and construction plans. Its intent is to prevent mistakes or fraud but the practice is not known to be effective.

Online usage.

In e-mail and newsgroup usage, another type of signature exists which is independent of one's language. Users can set one or more lines of custom text known as a signature block to be automatically appended to their messages. This text usually includes a name, contact information, and sometimes quotations and ASCII art. A shortened form of a signature block, only including one's name, often with some distinguishing prefix, can be used to simply indicate the end of a post or response. Some web sites also allow graphics to be used. Note, however, that this type of signature is not related to electronic signatures or digital signatures, which are more technical in nature and not directly understandable by humans. On Wikipedia, an online wiki-based encyclopedia edited by volunteers, the contributors "sign" their comments on talk pages with their username (only the username holder has the right to digitally affix their signature).

Art.

The signature on a painting or other work of art has always been an important item in the assessment of art. Fake signatures are sometimes added to enhance the value of a painting, or are added to a fake painting to support its authenticity. A notorious case was the signature of Johannes Vermeer on the fake "Supper at Emmaus" made by the art-forger Han van Meegeren. However, the fact that painters' signatures often vary over time (particularly in the modern and contemporary periods) might complicate the issue. The signatures of some painters take on an artistic form that may be of less value in determining forgeries.

Copyright.

Under British law, the appearance of signatures (not the names themselves) may be protected under copyright law.  Under United States copyright law, "titles, names [I c...]; mere variations of typographic ornamentation, lettering, or coloring" are not eligible for copyright; however, the appearance of signatures (not the names themselves) may be protected under copyright law.

Uniform Commercial Code.

Uniform Commercial Code §1-201(37) of the United States generally defines signed as "using any symbol executed or adopted with present intention to adopt or accept a writing." The Uniform Commercial Code §3-401(b) for negotiable instruments states "A signature may be made (i) manually or by means of a device or machine, and (ii) by the use of any name, including a trade or assumed name, or by a word, mark, or symbol executed or adopted by a person with present intention to authenticate a writing."

A signature (; from, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent. The writer of a signature is a signatory or signer. Similar to a handwritten signature, a signature work describes the work as readily identifying its creator. A signature may be confused with an autograph, which is chiefly an artistic signature. This can lead to confusion when people have both an autograph and signature and as such some people in the public eye keep their signatures private whilst fully publishing their autograph.


Life and work.

Vasarely was born in Pécs and grew up in Pöstyén (now Piešťany, Slovakia) and Budapest, where, in 1925, he took up medical studies at Eötvös Loránd University. In 1927, he abandoned medicine to learn traditional academic painting at the private Podolini-Volkmann Academy. In 1928/1929, he enrolled at Sándor Bortnyik's private art school called "Műhely" (lit. "Workshop", in existence until 1938), then widely recognized as Budapest's centre of Bauhaus studies. Cash-strapped, the "műhely" could not offer all that the Bauhaus offered. Instead it concentrated on applied graphic art and typographical design.  In 1929, he painted his "Blue Study" and "Green Study". In 1930, he married his fellow student Claire Spinner (1908–1990). Together they had two sons, Andre and Jean-Pierre. Jean-Pierre was also an artist and used the professional name 'Yvaral'. In Budapest, he worked for a ball-bearings company in accounting and designing advertising posters. Vasarely became a graphic designer and a poster artist during the 1930s combining patterns and organic images with each other.  Vasarely left Hungary and settled in Paris in 1930. He worked as a graphic artist and as a creative consultant at the advertising agencies Havas, Draeger, and Devambez (1930–1935). His interactions with other artists during this time were limited. He thought of opening an institution modelled after Sándor Bortnyik's "műhely" and developed some teaching material for it. Having lived mostly in cheap hotels, he settled in 1942/1944 in Saint-Céré in the Lot "département". After the Second World War, he opened an atelier in Arcueil, a suburb about 10 kilometres from the centre of Paris (in the Val-de-Marne "département" of the Île-de-France). In 1961, he finally settled in Annet-sur-Marne (in the Seine-et-Marne "département").  Vasarely eventually went on to produce art and sculpture using optical illusion. Over the next three decades, Vasarely developed his style of geometric abstract art, working in various materials but using a minimal number of forms and colours:  In October 1967, designer Will Burtin invited Vasarely to make a presentation to Burtin's Vision '67 conference, held at New York University. On 5 June 1970, Vasarely opened his first dedicated museum with over 500 works in a renaissance palace in Gordes (closed in 1996). A second major undertaking was the "Foundation Vasarely" in Aix-en-Provence, a museum housed in a distinct structure specially designed by Vasarely. It was inaugurated in 1976 by French president Georges Pompidou, two years after his death. Sadly the museum is now in a state of disrepair, several of the pieces on display have been damaged by water leaking from the ceiling. Also, in 1976 his large kinematic object "Georges Pompidou" was installed in the Centre Pompidou in Paris and the Vasarely Museum located at his birthplace in Pécs, Hungary, was established with a large donation of works by Vasarely. In the same decade, he took a stab at industrial design with a 500-piece run of the upscale "Suomi" tableware by Timo Sarpaneva that Vasarely decorated for the German Rosenthal porcelain maker's "Studio Linie". In 1982, 154 specially created serigraphs were taken into space by the cosmonaut Jean-Loup Chrétien on board the French-Soviet spacecraft Salyut 7 and later sold for the benefit of UNESCO. In 1987, the second Hungarian Vasarely museum was established in Zichy Palace in Budapest with more than 400 works.  He died age 90 in Paris on 15 March 1997.

Legacy.

A new Vasarely exhibit was mounted in Paris at Musée en Herbe in 2012.  In 2019, a temporary exhibition of Vasarely's work entitled "Le Partage des Formes" was displayed in the Centre Georges Pompidou in Paris.

Victor Vasarely (; born Győző Vásárhelyi, ; – ), was a Hungarian-French artist, who is widely accepted as a "grandfather" and leader of the Op art movement.


Construction and parts.

Compasses are usually made of metal or plastic, and consist of two parts connected by a hinge that can be adjusted to change the radius of the circle one wishes to draw. Typically one part has a spike at its end, and the other part a pencil, or sometimes a pen.

Handle.

The handle is usually about half an inch long. Users can grip it between their pointer finger and thumb.

Legs.

There are two types of legs in a pair of compasses: the straight or the steady leg and the adjustable one. Each has a separate purpose; the steady leg serves as the basis or support for the needle point, while the adjustable leg can be altered in order to draw different sizes of circles.

Hinge.

The screw on the hinge holds the two legs in its position; the hinge can be adjusted depending on desired stiffness. The tighter the screw, the better the compass’ performance.

Needle point.

The needle point is located on the steady leg, and serves as the center point of circles that have to be drawn.

Pencil lead.

The pencil lead draws the circle on a particular paper or material. Alternatively, an ink nib or attachment with a technical pen may be used.

Adjusting nut.

This holds the pencil lead or pen in place.

Uses.

Circles can be made by fastening one leg of the compasses into the paper with the spike, putting the pencil on the paper, and moving the pencil around while keeping the hinge on the same angle. The radius of the circle can be adjusted by changing the angle of the hinge.  Distances can be measured on a map using compasses with two spikes, also called a dividing compass. The hinge is set in such a way that the distance between the spikes on the map represents a certain distance in reality, and by measuring how many times the compasses fit between two points on the map the distance between those points can be calculated.

Compasses and straightedge.

Compasses-and-straightedge constructions are used to illustrate principles of plane geometry. Although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles. The most rigorous definition of this abstract tool is the "collapsing compass"; having drawn a circle from a given point with a given radius, it disappears; it cannot simply be moved to another point and used to draw another circle of equal radius (unlike a real pair of compasses). Euclid showed in his second proposition (Book I of the "Elements") that such a collapsing compass could be used to transfer a distance, proving that a collapsing compass could do anything a real compass can do.

Variants.

A beam compass is an instrument with a wooden or brass beam and sliding sockets, or cursors, for drawing and dividing circles larger than those made by a regular pair of compasses.  Scribe-compasses is an instrument used by carpenters and other tradesmen. Some compasses can be used to scribe circles, bisect angles and in this case to trace a line. It is the compass in the most simple form. Both branches are crimped metal. One branch has a pencil sleeve while the other branch is crimped with a fine point protruding from the end. A wing nut on the hinge serves two purposes: first it tightens the pencil and secondly it locks in the desired distance when the wing nut is turned clockwise.  Loose leg wing dividers are made of all forged steel. The pencil holder, thumb screws, brass pivot and branches are all well built. They are used for scribing circles and stepping off repetitive measurements with some accuracy.  A proportional compass, also known as a military compass or sector, was an instrument used for calculation from the end of the sixteenth century until the nineteenth century. It consists of two rulers of equal length joined by a hinge. Different types of scales are inscribed on the rulers that allow for mathematical calculation.  A reduction compass is used to reduce or enlarge patterns while conserving angles.

As a symbol.

A pair of compasses is often used as a symbol of precision and discernment. As such it finds a place in logos and symbols such as the Freemasons' Square and Compasses and in various computer icons. English poet John Donne used the compass as a conceit in "" (1611).

A compass, also known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.


Career.

From 1971–84, Mayor worked as a research associate at the Observatory of Geneva, which is home to the astronomy department of the University of Geneva. He became an associate professor at the university in 1984. In 1988, the university named him a full professor, a position he held until his retirement in 2007. Mayor was director of the Observatory of Geneva from 1998 to 2004. He is a professor emeritus at the University of Geneva.

Research.

Mayor's research interests include extrasolar planets (also known as exoplanets), instrumentation, statistical properties of double stars, globular cluster dynamics, galactic structure and kinematics. Mayor's doctoral thesis at the University of Geneva was devoted to the spiral structure of galaxies.  During his time as a research associate, there had been strong interest in developing photoelectric-based Doppler spectrometers to obtain more accurate measurements of radial velocities of stellar objects compared to existing photographic methods. Following preliminary work by Roger Griffin in 1967 to show the feasibility of photoelectric measurements of radial velocities, Mayor worked with André Baranne at the Marseille Observatory to develop COREVAL, a photoelectric spectrometer capable of highly accurate radial velocity measurements, which allow measurement of star movements, orbital periods of binary stars, and even the rotational speed of stars.  This research led to various fields of interest, including the study of statistical characteristics of solar-type binary stars. With fellow researcher Antoine Duquennoy, they examined the radial velocities of several systems believed to be binary stars in 1991. Their results found that a subset of these may in fact be single star systems with substellar secondary objects. Desiring more accurate radial velocity measurements, Mayor, along with Baranne at Marseille, and with graduate student Didier Queloz, developed ELODIE, a new spectrograph based on the work of CORAVEL, which was estimated to have an accuracy of 15 m/s for bright stars, improving upon the 1 km/s from CORAVEL. ELODIE was developed with the specific intent to determine if the substellar secondary objects were brown dwarf stars or potentially giant planets.  By 1994, ELODIE was operational at Geneva and Mayor and Queloz began their survey of Sun-like systems with suspected substellar secondary objects. In July 1995, the pair's survey of the 51 Pegasi affirmed that there was an exoplanet orbiting it, identified as 51 Pegasi b which was later classified as a Hot Jupiter-type planet. This was the first exoplanet to be found orbiting a main sequence star, as opposed to planets that orbited the remains of a star. Mayor's and Queloz's discovery of an exoplanet launched great interest is searching for other exoplanets since. As of 2019, there are at least 4000 confirmed exoplanet discoveries with several more potential candidates.  Mayor's work focused more on improving instrumentation for radial velocity measurements to improve detecting exoplanets and measuring their properties. Mayor led a team to further improve ELODIE to increase velocity measurement accuracy to 1 m/s via the High Accuracy Radial Velocity Planet Searcher (HARPS) installed on the ESO 3.6 m Telescope at La Silla Observatory in Chile by 2003. Mayor led the team that used HARPS to seek out other exoplanets. In 2007, Mayor was one of 11 European scientists who discovered Gliese 581c, the first extrasolar planet in a star's habitable zone, from the ESO telescope. In 2009, Mayor and his team discovered the lightest exoplanet ever detected around a main sequence star: Gliese 581e. Nonetheless, Mayor noted that humans will never migrate to such exoplanets since they are "much, much too far away... [and would take] hundreds of millions of days using the means we have available today". However, due to discoveries by Mayor, searching for extraterrestrial communications from exoplanets may now be a more practical consideration than thought earlier.

Awards and distinctions.

In 1998, Mayor was awarded the Swiss Marcel Benoist Prize in recognition of his work and its significance for human life. As of 2003, he was a member of the board of trustees. He received the Prix Jules Janssen from the Société astronomique de France (French Astronomical Society) in 1998.  In 2000, he was awarded the Balzan Prize. Four years later, he was awarded the Albert Einstein Medal. In 2005, he received the Shaw Prize in Astronomy, along with American astrophysicist Geoffrey Marcy. Mayor was made a knight of the French Legion d'Honneur in 2004.  In collaboration with Pierre-Yves Frei, Mayor wrote a book in French called "Les Nouveaux mondes du Cosmos" (Seuil, 260 pages), which was awarded the "Livre de l'astronomie 2001" prize by the 17th Astronomy Festival Haute Maurienne.  Mayor has received honorary doctorate degrees from eight universities: Katholieke Universiteit Leuven (Belgium), 2001; Swiss Federal Institute of Technology at Lausanne (EPFL) (2002); Federal University of Rio Grande do Norte (Brazil), 2006; Uppsala University (Sweden), 2007; Paris Observatory (France), 2008; Université Libre de Bruxelles (Belgium), 2009; University of Provence (Marseille, France), 2011, and Université Joseph Fourier (Grenoble, France), 2014.  Mayor has received the 2011 BBVA Foundation Frontiers of Knowledge Award of Basic Sciences (together with his former student Didier Queloz) for developing new astronomical instruments and experimental techniques that led to the first observation of planets around Sun-like stars. Asteroid 125076 Michelmayor, discovered by Swiss amateur astronomer Michel Ory at the Jura Observatory in 2001, was named in his honor. The official was published by the Minor Planet Center on 21 August 2013 ().  In 2015, he was awarded the Gold Medal of the Royal Astronomical Society. In 2017, he received the Wolf Prize in Physics. He and Didier Queloz (also from Switzerland) were awarded one half of the 2019 Nobel Prize in Physics for the discovery of the exoplanet 51 Pegasi b.

Michel Gustave Édouard Mayor (; born 12 January 1942) is a Swiss astrophysicist and professor emeritus at the University of Geneva's Department of Astronomy. He formally retired in 2007, but remains active as a researcher at the Observatory of Geneva. He is co-laureate of the 2019 Nobel Prize in Physics along with Jim Peebles and Didier Queloz, the 2010 Viktor Ambartsumian International Prize, and the winner of the 2015 Kyoto Prize.


Chemical properties.

The salt forms crystalline hydrates, unlike the other alkali metal chlorides. Mono-, tri-, and pentahydrates are known. The anhydrous salt can be regenerated by heating the hydrates. LiCl also absorbs up to four equivalents of ammonia/mol. As with any other ionic chloride, solutions of lithium chloride can serve as a source of chloride ion, e.g., forming a precipitate upon treatment with silver nitrate:

Preparation.

Lithium chloride is produced by treatment of lithium carbonate with hydrochloric acid. It can in principle also be generated by the highly exothermic reaction of lithium metal with either chlorine or anhydrous hydrogen chloride gas. Anhydrous LiCl is prepared from the hydrate by heating with a stream of hydrogen chloride.

Uses.

Lithium chloride is mainly used for the production of lithium metal by electrolysis of a LiCl/KCl melt at. LiCl is also used as a brazing flux for aluminium in automobile parts. It is used as a desiccant for drying air streams. In more specialized applications, lithium chloride finds some use in organic synthesis, e.g., as an additive in the Stille reaction. Also, in biochemical applications, it can be used to precipitate RNA from cellular extracts.  Lithium chloride is also used as a flame colorant to produce dark red flames.  Lithium chloride is used as a relative humidity standard in the calibration of hygrometers. At a saturated solution (45.8%) of the salt will yield an equilibrium relative humidity of 11.30%. Additionally, lithium chloride can itself be used as a hygrometer. This deliquescent salt forms a self-solution when exposed to air. The equilibrium LiCl concentration in the resulting solution is directly related to the relative humidity of the air. The percent relative humidity at can be estimated, with minimal error in the range, from the following first order equation: RH=107.93-2.11C, where C is solution LiCl concentration, percent by mass.  Molten LiCl is used for the preparation of carbon nanotubes, graphene and lithium niobate.  Lithium chloride has been shown to have strong acaricidal properties, being effective against "Varroa destructor" in populations of honey bees.

Precautions.

Lithium salts affect the central nervous system in a variety of ways. While the citrate, carbonate, and orotate salts are currently used to treat bipolar disorder, other lithium salts including the chloride were used in the past. For a short time in the 1940s lithium chloride was manufactured as a salt substitute, but this was prohibited after the toxic effects of the compound were recognized.

Lithium chloride is a chemical compound with the formula LiCl. The salt is a typical ionic compound, although the small size of the Li ion gives rise to properties not seen for other alkali metal chlorides, such as extraordinary solubility in polar solvents (83.05 g/100 mL of water at 20 °C) and its hygroscopic properties.


Life.

Enzensberger was born in 1929 in a small town in Bavaria and is the eldest of four boys. He is part of the last generation of intellectuals whose writing was shaped by first-hand experience of the Third Reich. The Enzensberger family moved to Nuremberg, the ceremonial birthplace of National Socialism, in 1931. Julius Streicher, the founder and publisher of Der Stürmer, was their next-door neighbour. Hans Magnus joined the Hitler Youth in his teens, but was expelled soon afterwards. "I have always been incapable of being a good comrade. I can't stay in line. It's not in my character. It may be a defect, but I can't help it."  Enzensberger studied literature and philosophy at the universities of Erlangen, Freiburg and Hamburg, and at the Sorbonne in Paris, receiving his doctorate in 1955 for a thesis about Clemens Brentano's poetry. Until 1957 he worked as a radio editor in Stuttgart. He participated in several gatherings of Group 47. Between 1965 and 1975 he lived briefly in the US and Cuba and edited the magazine "Das Kursbuch". Since 1985 he has been the editor of the prestigious book series "Die Andere Bibliothek", published in Frankfurt, and now containing almost 250 titles. Together with Gaston Salvatore, Enzensberger was the founder of the monthly "TransAtlantik". His own work has been translated into more than 40 languages.  Enzensberger is the older brother of the author Christian Enzensberger.  He lives in Munich.

Work.

Enzensberger has a sarcastic, ironic tone in many of his poems. For example, the poem "Middle Class Blues" consists of various typicalities of middle class life, with the phrase "we can't complain" repeated several times, and concludes with "what are we waiting for?". Many of his poems also feature themes of civil unrest over economic and class based issues. Though primarily a poet and essayist, he also makes excursions into theater, film, opera, radio drama, reportage, translation. He has written novels and several books for children (including "The Number Devil", an exploration of mathematics) and is co-author of a book for German as a foreign language "(Die Suche)". He also invented and collaborated in the construction of a machine which automatically composes poems. It was used during the 2006 Football World Cup to commentate on games.  With Irene Dische he wrote the libretto for Aulis Sallinen's fifth opera "The Palace".  In 2009, Enzensberger received a special Lifetime Recognition Award given by the trustees of the Griffin Trust for Excellence in Poetry, which also awards the annual Griffin Poetry Prize.

Hans Magnus Enzensberger (born 11 November 1929 in Kaufbeuren) is a German author, poet, translator and editor. He has also written under the pseudonym Andreas Thalmayr.


Biography.

Born in Ravensburg, in 1129 or 1131, he was the son of Henry the Proud, Duke of Bavaria and Saxony, who was the son of Duke Henry the Black and an heir of the Billungs, former dukes of Saxony. Henry's mother was Gertrude, only daughter of the Emperor Lothair III and his wife Richenza of Northeim, heiress of the Saxon territories of Northeim and the properties of the Brunones, counts of Brunswick.  Henry's father died in 1139, aged 32, when Henry was still a child. King Conrad III had dispossessed Henry the Proud of his duchies in 1138 and 1139, handing Saxony to Albert the Bear and Bavaria to Leopold of Austria. This was because Henry the Proud had been his rival for the Crown in 1138. Henry III, however, did not relinquish his claims to his inheritance, and Conrad returned Saxony to him in 1142. A participant in the 1147 Wendish Crusade, Henry also reacquired Bavaria by a decision of the new Emperor Frederick Barbarossa in 1156. However, the East Mark was not returned, which became Austria. Henry was the founder of Munich (1157; "München") and Lübeck (1159); he also founded and developed numerous other cities in Northern Germany and Bavaria, a.o. Augsburg, Hildesheim, Stade, Kassel, Güstrow, Lüneburg, Salzwedel, Schwerin and Brunswick. In Brunswick, his capital, he had a bronze lion, his heraldic animal, erected in the courtyard of his castle Dankwarderode in 1166 — the first bronze statue north of the Alps. Later, he had Brunswick Cathedral built close to the statue. In 1147, Henry married Clementia of Zähringen, thereby gaining her hereditary territories in Swabia. He divorced her in 1162, apparently under pressure from the Emperor Frederick Barbarossa, who did not cherish Guelphish possessions in his home area and offered Henry several fortresses in Saxony in exchange. In 1168, Henry married Matilda (1156–1189), the daughter of King Henry II of England and Duchess Eleanor of Aquitaine and sister of King Richard I of England.  Henry faithfully supported his older cousin, the Emperor Frederick I (Barbarossa), in his attempts to solidify his hold on the Imperial Crown and his repeated wars with the cities of Lombardy and the Popes, several times turning the tide of battle in Frederick's favor with his Saxon knights. During Frederick's first invasion of northern Italy, Henry took part, among the others, in the victorious sieges of Crema and Milan.  In 1172, Henry took a pilgrimage to Jerusalem (June–July), meeting with the Knights Templar and Knights Hospitaller, and spending Easter of that year in Constantinople. By December 1172, he was back in Bavaria and in 1174, he refused to aid Frederick in a renewed invasion of Lombardy because he was preoccupied with securing his own borders in the East. He did not consider these Italian adventures worth the effort, unless Barbarossa presented Henry with the Saxon imperial city Goslar: a request Barbarossa refused. Barbarossa's expedition into Lombardy ultimately ended in failure. He bitterly resented Henry for failing to support him. Taking advantage of the hostility of other German princes to Henry, who had successfully established a powerful and contiguous state comprising Saxony, Bavaria and substantial territories in the north and east of Germany, Frederick had Henry tried "in absentia" for insubordination by a court of bishops and princes in 1180. Declaring that Imperial law overruled traditional German law, the court had Henry stripped of his lands and declared him an outlaw. Frederick then invaded Saxony with an Imperial army to bring his cousin to his knees. Henry's allies deserted him, and he finally had to submit in November 1181 at an Imperial Diet in Erfurt. He was exiled from Germany in 1182 for three years, and stayed with his father-in-law in Normandy before being allowed back into Germany in 1185. At Whitsun 1184 he visited the Diet of Pentecost in Mainz, probably as a mediator for his father-in-law Heinrich II. He was exiled again in 1188. His wife Matilda died in 1189.  When Frederick Barbarossa went on the Crusade of 1189, Henry returned to Saxony, mobilized an army of his faithful, and conquered the rich city of Bardowick as punishment for its disloyalty. Only the churches were left standing. Barbarossa's son, Emperor Henry VI, again defeated the Duke, but in 1194, with his end approaching, he made his peace with the Emperor, and returned to his much diminished lands around Brunswick, where he finished his days as Duke of Brunswick, peacefully sponsoring arts and architecture.

Family.

Henry had the following known children:  Three other children are listed, by some sources, as having belonged to Henry and Matilda:  And by his lover, Ida von Blieskastel, he had a daughter:

Legacy.

The Henry the Lion Bible is preserved in near mint condition from the year 1170; it is located in the Herzog August Library in Wolfenbüttel, a town in Lower Saxony.  Henry the Lion remains a popular figure to this day. During World War I, a nail man depicting Henry the Lion, called "", was used in Brunswick to raise funds for the German war effort.  Nazi propaganda later declared Henry an antecessor of the Nazi's "Lebensraum" policy and turned Brunswick Cathedral and Henry's tomb into a "National Place of Consecration".

Henry the Lion in folklore and fiction.

Shortly after his death, Henry the Lion became the subject of a folktale, the so-called "Heinrichssage". The tale was later also turned into the opera "Enrico Leone" by Italian composer Agostino Steffani. The "Heinrichssage" details a fictional account of Henry's pilgrimage to the Holy Land. A popular part of the tale deals with the Brunswick Lion. According to legend, Henry witnessed a fight between a lion and a dragon while on pilgrimage. He joins the lion in its fight and they slay the dragon. The faithful lion then accompanies Henry on his return home. After its master's death, the lion refuses all food and dies of grief on Henry's grave. The people of Brunswick then erect a statue in the lion's honour. The legend of Henry the Lion also inspired the Czech tale of the knight, which is depicted on a column on Charles Bridge in Prague.  Henry the Lion featured as an ally and adversary of Barbarossa, and was eventually revealed to be the narrator of the Barbarossa campaign in the video game, "".

Henry the Lion (; 1129/1131 – 6 August 1195) was a member of the Welf dynasty and Duke of Saxony, as Henry III, from 1142, and Duke of Bavaria, as Henry XII, from 1156, the duchies which he held until 1180.


Right pyramids with a regular base.

A right pyramid with a regular base has isosceles triangle sides, with symmetry is C or [1,"n"], with order 2"n". It can be given an extended Schläfli symbol ( ) ∨ {"n"}, representing a point, ( ), joined (orthogonally offset) to a regular polygon, {n}. A join operation creates a new edge between all pairs of vertices of the two joined figures.  The trigonal or triangular pyramid with all equilateral triangle faces becomes the regular tetrahedron, one of the Platonic solids. A lower symmetry case of the triangular pyramid is C, which has an equilateral triangle base, and 3 identical isosceles triangle sides. The square and pentagonal pyramids can also be composed of regular convex polygons, in which case they are Johnson solids.  If all edges of a square pyramid (or any convex polyhedron) are tangent to a sphere so that the average position of the tangential points are at the center of the sphere, then the pyramid is said to be canonical, and it forms half of a regular octahedron.  Pyramids with a hexagon or higher base must be composed of isosceles triangles. A hexagonal pyramid with equilateral triangles would be a completely flat figure, and a heptagonal or higher would have the triangles not meet at all.

Right star pyramids.

Right pyramids with regular star polygon bases are called star pyramids. For example, the pentagrammic pyramid has a pentagram base and 5 intersecting triangle sides.

Right pyramids with an irregular base.

A right pyramid can be named as ( )∨P, where ( ) is the apex point, ∨ is a join operator, and P is a base polygon.  An isosceles triangle right tetrahedron can be written as ( )∨[( )∨{ }] as the join of a point to an isosceles triangle base, as [( )∨( )]∨{ } or { }∨{ } as the join (orthogonal offsets) of two orthogonal segments, a digonal disphenoid, containing 4 isosceles triangle faces. It has C symmetry from two different base-apex orientations, and C in its full symmetry.  A rectangular right pyramid, written as ( )∨[{ }×{ }], and a rhombic pyramid, as ( )∨[{ }+{ }], both have symmetry C.

Volume.

The volume of a pyramid (also any cone) is formula_1, where "b" is the area of the base and "h" the height from the base to the apex. This works for any polygon, regular or non-regular, and any location of the apex, provided that "h" is measured as the perpendicular distance from the plane containing the base. In 499 AD Aryabhata, a mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, used this method in the "Aryabhatiya" (section 2.6).  The formula can be formally proved using calculus. By similarity, the "linear" dimensions of a cross-section parallel to the base increase linearly from the apex to the base. The scaling factor (proportionality factor) is formula_2, or formula_3, where "h" is the height and "y" is the perpendicular distance from the plane of the base to the cross-section. Since the area of any cross-section is proportional to the square of the shape's scaling factor, the area of a cross-section at height "y" is formula_4, or since both "b" and "h" are constants, formula_5. The volume is given by the integral  The same equation, formula_1, also holds for cones with any base. This can be proven by an argument similar to the one above; see volume of a cone.  For example, the volume of a pyramid whose base is an "n"-sided regular polygon with side length "s" and whose height is "h" is  The formula can also be derived exactly without calculus for pyramids with rectangular bases. Consider a unit cube. Draw lines from the center of the cube to each of the 8 vertices. This partitions the cube into 6 equal square pyramids of base area 1 and height 1/2. Each pyramid clearly has volume of 1/6. From this we deduce that pyramid volume = height × base area / 3.  Next, expand the cube uniformly in three directions by unequal amounts so that the resulting rectangular solid edges are "a", "b" and "c", with solid volume "abc". Each of the 6 pyramids within are likewise expanded. And each pyramid has the same volume "abc"/6. Since pairs of pyramids have heights "a"/2, "b"/2 and "c"/2, we see that pyramid volume = height × base area / 3 again.  When the side triangles are equilateral, the formula for the volume is This formula only applies for "n" = 2, 3, 4 and 5; and it also covers the case "n" = 6, for which the volume equals zero (i.e., the pyramid height is zero).

Surface area.

The surface area of a pyramid is formula_10, where "B" is the base area, "P" is the base perimeter, and the slant height formula_11, where "h" is the pyramid altitude and "r" is the inradius of the base.

Centroid.

The centroid of a pyramid is located on the line segment that connects the apex to the centroid of the base. For a solid pyramid, the centroid is 1/4 the distance from the base to the apex.

"n"-dimensional pyramids.

A 2-dimensional pyramid is a triangle, formed by a base edge connected to a noncolinear point called an apex.  A 4-dimensional pyramid is called a polyhedral pyramid, constructed by a polyhedron in a 3-space hyperplane of 4-space with another point off that hyperplane.  Higher-dimensional pyramids are constructed similarly.  The family of simplices represent pyramids in any dimension, increasing from triangle, tetrahedron, 5-cell, 5-simplex, etc. A n-dimensional simplex has the minimum "n+1" vertices, with all pairs of vertices connected by edges, all triples of vertices defining faces, all quadruples of points defining tetrahedral cells, etc.

Polyhedral pyramid.

In 4-dimensional geometry, a polyhedral pyramid is a 4-polytope constructed by a base polyhedron cell and an apex point. The lateral facets are pyramid cells, each constructed by one face of the base polyhedron and the apex. The vertices and edges of polyhedral pyramids form examples of apex graphs, graphs formed by adding one vertex (the apex) to a planar graph (the graph of the base).  The regular 5-cell (or 4-simplex) is an example of a "tetrahedral pyramid". Uniform polyhedra with circumradii less than 1 can be make polyhedral pyramids with regular tetrahedral sides. A polyhedron with "v" vertices, "e" edges, and "f" faces can be the base on a polyhedral pyramid with "v+1" vertices, "e+v" edges, "f+e" faces, and "1+f" cells.  A 4D "polyhedral pyramid" with axial symmetry can be visualized in 3D with a Schlegel diagram—a 3D projection that places the apex at the center of the base polyhedron.  Any convex 4-polytope can be divided into polyhedral pyramids by adding an interior point and creating one pyramid from each facet to the center point. This can be useful for computing volumes.  The 4-dimensional "volume" of a polyhedral pyramid is 1/4 of the volume of the base polyhedron times its perpendicular height, compared to the area of a triangle being 1/2 the length of the base times the height and the volume of a pyramid being 1/3 the area of the base times the height.

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a "lateral face". It is a conic solid with polygonal base. A pyramid with an "n"-sided base has vertices, faces, and 2"n" edges. All pyramids are self-dual.


Biography.

Youth.

Barlach was born in Wedel, Holstein as the oldest of the four sons of Johanna Luise Barlach and Dr Georg Barlach. He attended primary school in Ratzeburg. It was during this period that his father died, early in 1884. He came from a Lutheran home.

Study years.

Barlach studied from 1888 to 1891 at the Gewerbeschule Hamburg. Due to his artistic talent, he continued his studies at the "Königliche Akademie der bildenden Künste zu Dresden" (Royal Art School Dresden) as a student of Robert Diez between 1891 and 1895. He created his first major sculpture during this time, "Die Krautpflückerin" (The Herb Plucker). He continued his studies for one more year in Paris at the Académie Julian, from 1895 to 1897 but remained critical of the German tendency to copy the style of French artists. Nevertheless, he returned to Paris again for a few months in 1897 to undertake further studies.

Seeking.

After his studies, Barlach worked for some time as a sculptor in Hamburg and Altona, working mainly in an Art Nouveau style. He produced illustrations for the Art Nouveau magazine Jugend 1897–1902, and made sculpture in a style close to Art Nouveau, including some ceramic statues. Afterwards, he also worked as a teacher at a school for ceramics. His first solo exhibition took place at the Kunstsalon Richard Mutz, Berlin, in 1904.

Formative years.

However, the lack of commercial success of his works depressed Barlach. To lighten up, he decided to travel for eight weeks together with his brother Nikolaus and to visit his brother Hans in Russia. This trip to Russia in 1906 was one of the greatest influences on him and his artistic style. Also during his travels in Russia his son Nikolaus was born on 20 August 1906, starting a two-year fight with the mother, Rosa Schwab, for the custody of the child, which Barlach was finally granted.  After returning from Russia, Barlach's financial situation improved considerably, as he received a fixed salary from the art dealer Paul Cassirer in exchange for his sculptures. The formative experiences in Russia and the financial security helped him to develop his own style, focusing on the faces and hands of the people in his sculptures and reducing the other parts of the figures to a minimum. He also began to make wood carvings and bronzes of figures swathed in heavy drapery like those in early Gothic art, and in dramatic attitudes expressive of powerful emotions and a yearning for spiritual ecstasy. He also worked for the German journal "Simplicissimus", and started to produce some literature. His works were shown on various exhibitions. He also spent ten months in Florence, Italy in 1909 and afterwards settled in 1910 in Güstrow in Mecklenburg, where he spent the rest of his life.  In the years before World War I, Barlach was a patriotic and enthusiastic supporter of the war, awaiting a new artistic age from the war. This support for the war can also be seen in his works, as for example the statue "Der Rächer" (The Avenger), from December 1914. His awaited "new artistic age" came for him when he volunteered to join the war between 1915 and 1916 as an infantry soldier. After three months of service he was discharged due to a heart ailment, returning as a pacifist and a staunch opponent of war. The horror of the war influenced all of his subsequent works.

Popularity.

Barlach's fame increased after the war, and he received many awards and became a member in the prestigious "Preußische Akademie der Künste" (Prussian Art Academy) in 1919 and the "Akademie der Bildenden Künste München" (Munich Art Academy) in 1925. Barlach rejected a number of honorary degrees and teaching positions. In 1925 he also met Bernhard and Marga Böhmer for the first time. He received the Kleist Prize for drama in 1924 for his "Die Sündflut" ("The Flood"), in which he projects his personal mysticism onto the story of Noah and the Ark. In 1926 he wrote "Der blaue Boll" (translated as "Squire Blue Boll" or "Boozer Boll"), an expressionist drama in which the eponymous squire almost succeeds in seducing a down-and-out young mother, before both achieve spiritual regeneration.

Degenerate art.

From 1928 onward Barlach also generated many anti-war sculptures based on his experiences in the war. This pacifist position went against the political trend during the rise of Nazism, and he was the target of much criticism. For example, the "Magdeburger Ehrenmal" (Magdeburg cenotaph) was ordered by the city of Magdeburg to be a memorial of World War I, and it was expected to show heroic German soldiers fighting for their glorious country. Barlach, however, created a sculpture with three German soldiers, a fresh recruit, a young officer and an old reservist, standing in a cemetery, all bearing marks of the horror, pain and desperation of the war, flanked by a mourning war widow covering her face in despair, a skeleton wearing a German army helmet, and a civilian (the face is that of Barlach himself) with his eyes closed and blocking his ears in terror. This naturally created a controversy with the pro-war population (several nationalists and Nazis claimed that the soldiers must be foreign since true Germans would be more heroic), and the sculpture was removed. Friends of Barlach were able to hide the sculpture until after the war, when it was returned to the Magdeburg Cathedral. Yet the attacks on Barlach continued until his death.  In 1931 Barlach started to live with Marga Böhmer, whereas her ex-husband and Barlach's friend Bernhard Böhmer lived with his new wife Hella.  In 1936, Barlach's works were confiscated during an exhibition together with the works of Käthe Kollwitz and Wilhelm Lehmbruck, and the majority of his remaining works were confiscated as "degenerate art", for example the "Güstrower Ehrenmal" (Güstrow cenotaph) and the "Hamburger Ehrenmal" (Hamburg cenotaph). Barlach himself was prohibited from working as a sculptor, and his membership in the art academies was canceled. This rejection is reflected in his final works before his death from heart failure on 24 October 1938 in Rostock, Mecklenburg. He is buried in the cemetery of Ratzeburg.  In addition to his sculpture, Barlach also wrote eight Expressionist dramas, two novels and an autobiography "Ein selbsterzähltes Leben" 1928, and had a distinguished oeuvre of woodcuts and lithographs from about 1910 onwards, including illustrations for his own plays.

Selected works.

Sales.

On 2 May 2012, Barlach's carved wood sculpture "Weinende Frau" sold at Christie's for $938,500, setting a new world auction record for a price paid for Barlach's work.

Ernst Barlach (2 January 1870 in Wedel – 24 October 1938 in Rostock) was a German expressionist sculptor, printmaker and writer. Although he was a supporter of the war in the years leading to World War I, his participation in the war made him change his position, and he is mostly known for his sculptures protesting against the war. This created many conflicts during the rise of the Nazi Party, when most of his works were confiscated as degenerate art.