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# Asteroids That Have Hit Earth

The first step to protect ourselves is therefore detection, tracking and risk assessment. In 2013, Nasa calculated that Apophis would not hit Earth. It was a tight squeeze, and media were paying attention. Objects like Bennu are thought to be composed of hydrated minerals like clays and organic material. If you see this message, your browser is not compatible. This is not a big asteroid, but Asteroid 2005 YU55, a 1,300-foot monster, passed within 200,000 miles of the Earth on November 8, 2011. NASA/GSFC/USGS/JPL An inbound asteroid approaches the Earth-moon system. Earth may be. 2 mile diameter asteroid named (89959) 2002 NT7 was in fact assigned a positive impact rating on the Palermo Technical Impact Hazard Scale , meaning that the object will likely strike earth on some future date. If it strikes a populated area is could wipe out entire cities and. Having no atmosphere, it is totally exposed to meteoroids. Dangerous asteroids flying past Earth are not rare, and more meteor strikes happen than the public is aware of, the head of NASA has said. Asteroid 2006 QV89 has a diameter of 164 feet and will make its closest pass to earth on September 9, 2019. But asteroids still only hit Earth on average every million or few million years, even with the increased crash rate. It doesn't have to be huge — a couple of tons, not that big — and you park it near the asteroid. The space agency is sending a probe to collect rock samples from. The following table summarizes by object the potential future Earth impact events that the JPL Sentry System has detected based on currently available observations. Some asteroids have very elliptical trajectories, crossing the orbits of the inner planets Mars, Earth or Venus. This early evening Arizona time it will have reached magnitude 9. The situation will become clearer once more precise data on the rock's orbit in the Solar. Most of them burn up before reaching the atmosphere and perish, but the ones that do hit usually hit the water because 70% of. The truth behind doomsday rumours. We are being hit by small comets and asteroids in the hundreds every day. 2016 PD1 is currently travelling at a speed of 13,000mph and has an estimated diameter of 360ft. Near-Earth asteroids, or NEAs, are asteroids that have orbits that pass close to that of Earth. Observations have revealed almost 1,000 asteroids larger than a kilometer in near-Earth orbits. Scientists have found evidence that asteroids have hit our planet in the past. Astronomers around the world continue to work to monitor any asteroids that pose danger to us. 1996), looking at the composite of the earth on three arid site and considering the weathering over time, finds that between 36 and 116 meteorites over 10 g hit Earth every year per $10^6\,\mathrm{km}^2$. 2000 SG344 is part of a group called the Aten Asteroids, which have orbits aligned very closely with Earth’s. ") Now we have the assertion, based on a computer simulation by Australian engineer Michael Paine, that during the last 10,000 years, Earth was hit about 350 times by. ADVERTISEMENT At closest approach and with dark skies, 2019 OK would have been visible with a pair of binoculars as point of light. ASTEROID Bennu could hit Earth at 25 MILLION kph with the power of more than 76,000 Hiroshima nuclear bombs, creating a ball of fire as big as 20 …. But to give you some perspective, the asteroids will be closer to earth than the moon is, on July 24. Earth has a long list of hits—and not of the musical variety, but of the rocky, celestial sort. What is the chance of Earth being hit by a comet or asteroid? Not much in our lifetimes -- perhaps 1 in 10,000 -- but over thousands or millions of years, major impacts become pretty likely. Our solar system formed from a planetary nebula of dust and gas that slowly coalesced into rocks, planets, moons, and the Sun. Such bodies impact the Earth only once every 100,000 years on average. These small space rocks that have been chipped off of other planets such as Saturn or Mars are a great way of studying other planets surfaces without having to travel millions of miles for samples. Our entire military fleet is currently at war with the Martians and, as fate would have it, the asteroid field is too far away from Mars to reassign a Commander. So when we view the evidence from a biblical perspective, we recognize that these events occurred during the Flood just over 4,300 years ago, not 66 million. The Chicxulub crater is the most famous, because it is believed to have wiped out the dinosaurs and allowed mammals to evolve. Notably, NASA’s asteroid trackers have warned the asteroid risks striking the Earth on 28th December 2019 – if it suddenly veers off-course for some reason. Most asteroids are located in the asteroid belt and stay between the orbits of Mars and Jupiter which is very far from us. One of the least eroded, best preserved examples is the Barringer Meteor Crater near Winslow, Arizona. Large-scale asteroids hit Earth 3 to 10 times more than earlier revealed. But it was not until recently that this discovery was made. There are some 25,000 near-Earth asteroids with diameters more than 140 meters. But not to worry, if anything bigger than about 100 miles in diameter (guessing there, but I don't think it wouldn't have to be 1,000 miles-plus -- the Moon is 2,160 miles in diameter) hit the Earth, it would blow the atmosphere completely away. That approach could change Bennu’s course, putting it in a position to. Like rock stars, asteroids have been given their fair share of urban myth and lore. First you have to find all the asteroids, calculate their orbits and see which ones come dangerously close to Earth. The risk has been estimated by one expert as one in a million - but that is enough for scientists to be taking it extremely seriously. Large asteroids have been striking Earth more than twice as often in the past 290 million years than in the previous 700 million years, according to a new study published Thursday in the journal. Until now, many asteroids have hit Earth at different times. A little warning would have been nice. Several hundred more are discovered each year. Asteroids aren’t the only things that hit Earth. They have been found from inside Earth's orbit out to beyond Saturn's orbit. An asteroid impact—or several simultaneous impacts—that triggered the Flood may also have been part of an ongoing, solar-system-wide catastrophe that lasted for months or years. Many contain iron-nickel metal as a minor component. A visualisation of new data showing the surprising frequency at which the Earth is hit by asteroids has been released. Near Earth Objects & Impact Effects Near Earth Objects are asteroids or comets that have orbits around the Sun that bring them close to the Earth. Bennu could hit Earth with the power of 76,000 WW2 nuclear bombs and create 20km fireball. "A 10-inch meteoroid would disintegrate in mid-air, making a spectacular fireball in the sky but no crater. You have already voted for this video. an impact threat well into the future and the potential effects that it could have on Earth," NASA's planetary defense officer. Some have orbits that cross Earth's path, and there is evidence that Earth has been hit by asteroids in the past. Each day, more than 100 tons of material from asteroids and comets falls toward Earth. Follow TV Tropes. A widely-accepted theory is that a large asteroid hit Earth 65 million years ago and killed off about 50% of all life on Earth. Now we have the assertion, based on a computer simulation by Australian engineer Michael Paine, that during the last 10,000 years, Earth was hit about 350 times by asteroids as large as the rock that wasted 2,000 square kilometers of Siberian forest in 1908. They are classified into three broad families, Aten, which have a semi-major axis of less than one astronomical unit, Apollo, which cross the orbit of the Earth with a period exceeding one year. Why do comets and asteroids come close to Earth? -Asteroids usually have circular orbits that typically remain between Mars and Jupiter (and close to mars) unless Jupiter knocks the asteroid out of orbit (gravitational PERTURBATION) or the asteroid collides with another asteroid. Most Destructive Asteroid Impacts in Human History Experts and scientist researchers have stated that in the past 600 million years, about 60 asteroids or similar objects of 3 miles or larger in size have hit the earth. Heavy bombardments may have continued until as recently as 4 billion years ago, making it difficult for life to get a foothold at all (the "Late Heavy Bombardment"). Earth-crossing asteroids pose a very real (if statistically unlikely) danger to the Earth. With just a 50-meter diameter, it’s relatively small but is still twice as big as the Chelyabinsk meteor which caused so much damage six years ago. Yes, many asteroids have hit planet Earth in the last thousand years. Can an asteroid hit Earth? It is possible that an asteroid may hit Earth one day, but the chances of this happening are very small. Will asteroid Apophis hit Earth in 2036 and cause the apocalypse? The truth behind doomsday rumours. Gliese 710 is currently plunging through space at almost 32,000 mph (51,499 km/h), but gladly it is almost 64 light-years away. The European Space Agency (ESA) has warned that Earth has a chance of getting hit by an asteroid three years from now. Asteroids can be found orbiting the Sun in a belt between Mars and Jupiter; this is called the Asteroid belt or Main belt. Some asteroids go in front of and behind Jupiter. Good news: Last year saw a dramatic increase in the number of asteroids that we know about that flew uncomfortably close to the Earth, and 2018 is poised to see the highest amount of "potentially. Click on the object designation to go to a page with full details on that. At Ceres, the largest asteroid in the asteroid belt, there was a great deal of interest in very bright white spots on the surface of Ceres. I'm strictly interested in real doom porn so I only check the ones slated to come as close as one lunar distance or less. The same cannot be said of asteroids we don't know about, of course. Typical impact velocities are 17 km/s for asteroids and 51 km/s for comets. Consequently, astronomers across the globe have devoted considerable effort to determining the level of threat posed by near-Earth asteroids, and to identifying individual asteroids that could. An Asteroid Big Enough to Wipe Out a City Nearly Hit Earth Last Week. Like rock stars, asteroids have been given their fair share of urban myth and lore. Investigate the properties of Earth that hide past cratering events -- movement of the crust, erosion, water, and a protective atmosphere. And there are a lot of objects to find. Three asteroids are heading towards the Earth today and one will pass between the Earth and the moon's orbit. Asteroids occasionally hit Earth, and a sufficiently large asteroid could cause enormous humanitarian damage. What if an asteroid was about to hit Earth. Good news: Last year saw a dramatic increase in the number of asteroids that we know about that flew uncomfortably close to the Earth, and 2018 is poised to see the highest amount of "potentially. 6 days ago America's largest asteroid impact left a. Evidence that comets and asteroids still hit planets was witnessed by thousands in 1994 when come Shoemaker-Levy 9 smashed into the planet Jupiter with the force of thousands of hydrogen bombs. The Search for Extraterrestrial Life is about to go underwater. All known Potentially Hazardous Asteroids have less than a 0. There are lots of asteroids in our solar system. How many meteorites hit the earth each year, and how do they determine that? It's a bit hard to tell exactly how many meteorites hit Earth each year. In terms of space the moon is rubbing elbows to the earth. For asteroids coming in at 20 km/sec, it's generally thought that to penetrate the atmosphere and cause major damage by tsunami, an iron asteroid must be around 40 to 60 meters in diameter, and a stony asteroid 200 meters in diameter. Details here, including a recent, fortunate non-detection of the asteroid by ESA and ESO. In the visualization above, you can see the location of 26 space rocks that slammed into our planet between 2000. Tomorrow, another asteroid -- 2007 WD5 -- will. metres wide or more. Small objects frequently collide with the Earth. This tells you how much warning time you have. Recent studies have shown that the Earth has been hit an alarmingly large number of times in the past. "Mercury-Venus-Earth-Mars-Jupiter-Saturn-Uranus-Neptune Explosion"): Woz creates energy constructs resembling the 8 planets in the solar system that then disperse into energy asteroids and rain down upon any enemies within range of the asteroids' hits. The evidence, which will presented by three former Nasa employees, including two astronauts, will reveal the full extent of the explosions which they claim have shaken countries across the world. 2016 PD1 is currently travelling at a speed of 13,000mph and has an estimated diameter of 360ft. Most asteroids are found in the asteroid belt, but not all. They calculated that the asteroid, estimated between two and four kilometres in diameter, had a one in 60,000 chance of hitting Earth on February 1, 2019. My first asteroid-related project was as a college sophomore, 30 years ago, measuring the motion of Ceres across the sky. Planetary Defense is a complex problem, not well understood by policy makers and the general public. C-type or carbonaceous asteroids are dark from the high content of carbon in them. NASA/GSFC/USGS/JPL An inbound asteroid approaches the Earth-moon system. In fact, asteroids have slammed into our planet and caused cataclysmic damage many times in its. Chicxulub is the largest crater known which seems definitely to have an impact origin, but there are a few ring-like structures that are 2-3 times larger yet about which geologists are uncertain. One of the few asteroids that could hit Earth is Bennu, and CNEOS predicts it won't come close to Earth again until 2135. When an asteroid struck the Yucatan region about 66 million years ago, it wiped out the dinosaurs, and most of life on Earth. Science News NASA's very real plan to blow up asteroids and meteoroids threatening Earth with nuclear. "Earth's atmosphere protects us," Cooke explains. Such events happen once or twice yearly, astronomers say. Asteroid 2006 QV89 has a diameter of 164 feet and will make its closest pass to earth on September 9, 2019. The asteroids capable of causing a global disaster if they hit the Earth are extremely rare. Sometimes, because of the attraction of other planets, these asteroids change their orbit and collide with other asteroids. Meteorites hit the earth anywhere from every day to once in 10,000 years, depending on their size. They have been trying to think up plans to deal with a potential strike. The Tunguska asteroid strike of 1908 — about 40 meters in size — if it had hit New York would have obliterated its population and vital infrastructure. And yes, a larger deadly asteroid could eventually strike. Earth is a spaceship, and the Amazon is a crucial part of our life-support system, creating up to 20% of our o ctpost. Most meteors that you see in the sky are caused by pea-sized pieces of rock and there's a lot of stuff this size in the solar system that Earth can run into!. The object, dubbed Asteroid 2019 OK, missed the earth by about 70,000 kms, placing it closer to Earth than the moon. A little warning would have been nice. But it was not until recently that this discovery was made. Scientists have discovered a massive asteroid that is on course to hit the Earth next week, and are scrambling to find a way to divert the object. In the past few decades, astronomers have spotted more than 12,000 of them. The Earth had a brush with an object estimated to be around 20 metres across almost five years ago over Chelyabinsk in Russia. See where asteroids have hit Earth since 2001 1:00PM BST 22 Apr 2014. Still, a 300-meter object might have a global impact, causing a week or two of climate disruption and could kill crops in the northern hemisphere if it struck while crops were growing. Tech & Science asteroid day NASA Comets. With large groups, it is good to have at least two presenters. The number of asteroids hitting Earth and the moon have increased over the past 290 million years, research suggests. A Russian scientist has discovered a huge asteroid '2014 UR116' passes Earth every three years. The asteroids are orbiting the Sun, each one traveling around the Sun fast enough for the orbits not to degrade. which will rendezvous with asteroids and touch. A small number of meteorites have been shown to be of Lunar (23 finds) or Martian (22) origin. As of June 2016 [update] , 14,464 near-Earth asteroids are known [33] and the number over one kilometer in diameter is estimated to be 900–1,000. Gallinger said that if either the Tunguska or Chelyabinsk asteroids had been on a different trajectory, they might have made it to the earth’s surface causing even more damage. The peanut-shaped 2015 BN590 asteroid is a potentially hazardous object that might one day hit Earth. Yes, a killer asteroid could hit Earth | Popular Science Skip to main content. In 1998, the Congress told NASA to find the near-Earth asteroids larger than a kilometer in size within 10 years, and in 2005, This Asteroid Will Not Hit Earth. Meteorites hit the earth anywhere from every day to once in 10,000 years, depending on their size. The Chicxulub crater is the most famous, because it is believed to have wiped out the dinosaurs and allowed mammals to evolve. So when we view the evidence from a biblical perspective, we recognize that these events occurred during the Flood just over 4,300 years ago, not 66 million. Jun 16, 2016 · Another asteroid, Apophis, got a lot of attention from space scientists and the media when initial calculations indicated a small chance it could hit Earth in 2029 or 2036. The bombardment of Earth nearly 4 billion years ago by asteroids as large as Kansas would not have had the firepower to extinguish potential early life on the planet and may even have given it a boost, says a new University of Colorado at Boulder study. Once every few million years, an object large enough to threaten life on Earth comes along. Research by international scientists concluded that giant asteroids, similar or larger than the one believed to have killed the dinosaurs, hit Earth billions of years ago with more frequency than previously thought, U. Most of them burn up before reaching the atmosphere and perish, but the ones that do hit usually hit the water because 70% of. NASA prepares to nuke asteroid Bennu, threatening to hit Earth in 2135. When an asteroid struck the Yucatan region about 66 million years ago, it wiped out the dinosaurs, and most of life on Earth. But to give you some perspective, the asteroids will be closer to earth than the moon is, on July 24. 2011 AG5 is being studied by the UN Action Team on near-Earth objects. Theia formed in a Lagrange point, a gravitationally stable region in the Earth's orbit, located on the opposite side of the Sun. If you see this message, your browser is not compatible. Similarly, scientists had also just discovered that asteroid a couple of hours before it hit, but it wasn't nearly as large as 2019 OK. The object, dubbed Asteroid 2019 OK, missed the earth by about 70,000 kms, placing it closer to Earth than the moon. Multiple flyby missions to Comet Halley. On Monday, September 9, 2019, an asteroid about 40 meters in diameter could hit the planet Earth at 44,000 kilometers per hour. Currently, we have a few different telescopes here on Earth devoted to spotting near-Earth objects (the Catalina Sky Survey and. 11 comets and asteroids have been explored by spacecraft so far, as follows: ICE flyby of Comet Giacobini-Zinner. Large asteroids have been striking Earth more than twice as often in the past 290 million years than in the previous 700 million years, according to a new study published Thursday in the journal. In 2005, Congress directed NASA to evaluate the asteroid danger and to report on methods to survey for dangerous asteroids and on ways to divert those on a course for Earth (the George E. , the Barringer Meteor Crater in Arizona is only 50,000 years old). SpaceX CEO Elon Musk said that a large asteroid will eventually hit Earth and his concern is that "we currently have no defense" against it. 5 billion years ago. Over 19,000 near-earth asteroids have been mapped and studied by the Centre as of 2019, according to a report. NASA says there are no asteroids or comets observed that pose a threat of impact in the foreseeable future and estimates the chance of a PHO collision in the next century at less than 0. Asteroids that almost hit our planet - A large meteor, 10 times more powerful than the Hiroshima atomic bomb, exploded in the Earth's atmosphere on December 18, 2018. Massive Asteroid to Hit Earth in 2040? while researchers have better preliminary orbit data for 2011 AG5 than for many other asteroids in the NEO catalog, "we have only medium confidence in. Most of them live in the main asteroid belt —a region between the orbits of Mars and Jupiter. It was said there was an extremely low chance that it would hit Earth on February 1, 2002 and conspiracy nuts just said it would hit. The Taurids meteor. However unlikely a collision is, a large asteroid would likely wipe out life as we know. But not to worry, if anything bigger than about 100 miles in diameter (guessing there, but I don't think it wouldn't have to be 1,000 miles-plus -- the Moon is 2,160 miles in diameter) hit the Earth, it would blow the atmosphere completely away. Heavy bombardments may have continued until as recently as 4 billion years ago, making it difficult for life to get a foothold at all (the "Late Heavy Bombardment"). If you see this message, your browser is not compatible. Tunguska-type hits are rare—even smaller asteroids like 2012 DA14 strike the planet only once every 1,200 years or so. Asteroids have been hitting the Earth for billions of years. Asteroid Will Hit Earth Eventually, We Have No Defence Yet: Elon Musk A monster asteroid called Apophis -- named after an Egyptian "God of Chaos" -- will come dangerously close to the Earth, about. 1,000-Foot-Wide Asteroids That Could Hit Earth, Discovered by Astronomers June 11, 2017 Admin Scientists have discovered a new branch of the Taurids meteor stream that could pose a major risk to Earth, with asteroids up to 1,000 feet wide flying past us every few years. Large asteroids have hit Earth dozens of times in the distant past. 2 million km on 25 May 2019. In 1998, the Congress told NASA to find the near-Earth asteroids larger than a kilometer in size within 10 years, and in 2005, This Asteroid Will Not Hit Earth. But there have been other theorized impacts before that, and there is evidence on Earth of smaller asteroid impacts all the time (e. 2 miles in size are capable of wiping out life on Earth, but the last one known to hit was 66 million years ago which destroyed 75 per cent of all life, including the dinosaurs. Asteroid 2006 QV89 has a diameter of 164 feet and will make its closest pass to earth on September 9, 2019. Asteroids that could potentially hit Earth would most likely fall in the ocean, the report adds, which could have serious ramifications for populated coastal areas. We have been getting a lot of close calls with asteroids of late, with each one drifting ever nearer our terrestrial space. Jul 28, 2014 · Dinosaurs might have survived the catastrophic impact that ended their reign had the devastating asteroid that slammed into the Earth arrived at a "more convenient time", a scientist has claimed. “NASA has been in this business of finding near-Earth objects, asteroids and comets for a little over 15 years now,” Johnson says. If a chunk of this asteroid were to hit your your client’s home, they would. The atmosphere-free, 3. "It's a city-killer asteroid. Asteroids are classified according to their composition, size, or location. How many meteorites hit the earth each year, and how do they determine that? It's a bit hard to tell exactly how many meteorites hit Earth each year. Highlight Links. But of course, the samples that Hayabusa plucked from Itokawa’s surface in 2005 have been through a lot in the eons. There is absolutely no chance that asteroid 2012 DA14 will hit Earth when it makes its closest approach on Friday, Feb. Many contain iron-nickel metal as a minor component. But there have been other theorized impacts before that, and there is evidence on Earth of smaller asteroid impacts all the time (e. Galileo - NASA Mission to Jupiter via asteroids Gaspra and Ida; Future Missions. What's more, as The Daily Star reports, it is a 100 percent certainty that it's going to happen. 3 miles in length headed for earth. If you see this message, your browser is not compatible. About 30 small asteroids a few meters in size hit Earth every year. But it was not until recently that this discovery was made. Currently, about 150 new asteroids are discovered every month. Here are six of the closest approaches asteroids have made to Earth in recent memory. They have been trying to think up plans to deal with a potential strike. The Earth had a brush with an object estimated to be around 20 metres across almost five years ago over Chelyabinsk in Russia. Dangerous asteroids flying past Earth are not rare, and more meteor strikes happen than the public is aware of, the head of NASA has said. "A 10-inch meteoroid would disintegrate in mid-air, making a spectacular fireball in the sky but no crater. 14 and r is half the diame 0 Comments Add a Comment. Will asteroid Apophis hit Earth in 2036 and cause the apocalypse? The truth behind doomsday rumours. "Because of this, threatening to hit Earth in 2135. Amateur astronomers can find them — and the Planetary Society can help. There are lots of asteroids in our solar system. “It’s 100 percent certain we’ll be hit, but we’re not 100. But we do, and we need to use it’ Dangerous asteroids flying past Earth. Gallinger said that if either the Tunguska or Chelyabinsk asteroids had been on a different trajectory, they might have made it to the earth’s surface causing even more damage. Consequently, astronomers across the globe have devoted considerable effort to determining the level of threat posed by near-Earth asteroids, and to identifying individual asteroids that could. The following table summarizes by object the potential future Earth impact events that the JPL Sentry System has detected based on currently available observations. Another asteroid, Apophis, got a lot of attention from space scientists and the media when initial calculations indicated a small chance it could hit Earth in 2029 or 2036. Currently, we have a few different telescopes here on Earth devoted to spotting near-Earth objects (the Catalina Sky Survey and. NASA estimates that asteroids big enough to cause catastrophic destruction could theoretically hit Earth every million years, or at longer intervals. The obvious-seeming answer is that Earth’s gravity is to blame for all this imbalance, but there is no physically plausible way to make the connection. NASA Spots Five Asteroids That Will Be Flying Awfully Close to Earth Starting in July. By comparison, asteroids that populate the main asteroid belt between Mars and Jupiter, and pose no threat to Earth, can be as big as 940 kilometers (about 583 miles) across. There are only four asteroids and four comets at this size. According to a list of the most concerning space objects complied by the European Space Agency, an asteroid, known as 2006 QV89, with a. Observations by astronomers tracking near-Earth asteroids have raised a new object to the top of the Earth-threat list. In fact, asteroids have slammed into our planet and caused cataclysmic damage many times in its. The first step to protect ourselves is therefore detection, tracking and risk assessment. The fragments that break off as a result of this collision and fall to earth without being burned up are called meteorites. The newly discovered threat to global civilisation is called 2000. The potential mineral wealth of these asteroids is so great that huge profits could be made once we can start mining them for materials to be sold to markets on Earth. NASA has recently reported on asteroids entering the Earth's orbit, one of which even got closer to our planet than the moon. It is believed that as much as 10% of the Near-Earth Objects are actually extinct comet nuclei. NASA prepares to nuke asteroid Bennu, threatening to hit Earth in 2135. Asteroids that come close to Earth are called Near Earth Objects, NEOs for short. When a meteoroid, comet, or asteroid enters Earth's atmosphere at a speed typically in excess of 20 km/s (72,000 km/h; 45,000 mph), aerodynamic heating of that object produces a streak of light, both from the glowing object and the trail of glowing particles that it leaves in its wake. With just a 50-meter diameter, it’s relatively small but is still twice as big as the Chelyabinsk meteor which caused so much damage six years ago. 8 billion years ago. Near-Earth Object Survey Act). It is believed that as much as 10% of the Near-Earth Objects are actually extinct comet nuclei. com reported. An asteroid 1 km in size kicks so much dust into the atmosphere that sunlight would be blocked for several years, resulting in a global agricultural catastrophe. com - Morgan McFall-Johnsen, provided by • Record-breaking fires have hit the Amazon rainforest this year, most of which were lit by people clearing land for farming. More asteroids are smacking Earth. Our solar system formed from a planetary nebula of dust and gas that slowly coalesced into rocks, planets, moons, and the Sun. NASA reports that all of the near-earth asteroids as large as the one believed to have killed the dinosaurs have been detected, and substantial progress has been made in detecting other dangerously large asteroids. Click on the object designation to go to a page with full details on that. However, many of the NEAs have a darker, more de structive potential as well. 5 billion years ago. The small near-Earth asteroids 2008 TC 3, 2014 AA, and 2018 LA are the only three asteroids discovered before impacting into Earth (see Asteroid impact prediction). 6 mile-wide rock swings very close to the Sun, rapidly heating the asteroid's surface, and — scientists believe — creating fractures in its surface as its temperature changes, thus releasing dust. The same cannot be said of asteroids we don't know about, of course. The views expressed by contributors are their own and not the view of The Hill A new poll shows that more Americans think detecting asteroids headed for Earth is our top priority in space, rather. If we see an asteroid that's going to hit the Earth and we have enough time, we can hit it to move it into a better orbit. If something DOES hit the ground, it is known as a meteorite. The dinosaurs, which would have had little resistance to these new diseases, would have declined in population. ADVERTISEMENT At closest approach and with dark skies, 2019 OK would have been visible with a pair of binoculars as point of light. Aten asteroids -- whose orbits also cross Earth's orbit, but unlike Apollos, Atens spend most of their time inside Earth. “Almost all of the objects that hit the Earth originate for the solar system,” Loeb explained. For objects that cause major damage if they hit Earth (larger than about 30 meters), there are about a million. Yes, not only could an asteroid hit Earth, but many asteroids have already struck Earth. Nasa experts have found evidence that large-scale asteroids have struck Earth three to ten times more often over the past decade than previously thought. Large-scale asteroids hit Earth 3 to 10 times more than earlier revealed. Scientists have discovered a new branch of the Taurids meteor stream that could pose a major risk to Earth, with asteroids up to 1,000 feet wide flying past us every few years. Could Asteroids Bombard the Earth to Cause a Mass Extinction in 10 Million Years? Given the evidence that an asteroid triggered the dinosaur extinction, it makes sense to ask whether showers of. Other big asteroids have hit Earth in the past, leaving their marks in the Chesapeake Bay and in western Bavaria in Germany, for instance. If you see this message, your browser is not compatible. NASA Warns That Many Catastrophic Asteroids Will Hit Earth in the Near Future. The obvious-seeming answer is that Earth’s gravity is to blame for all this imbalance, but there is no physically plausible way to make the connection. What if an asteroid was about to hit Earth. SpaceX CEO Elon Musk said that a large asteroid will eventually hit Earth and his concern is that "we currently have no defense" against it. As of July 27 2011, thousands of asteroids have been discovered near Jupiter's L4 and L5 points, and four at Mars' and seven at Neptune's. An Asteroid Will Hit Earth Again at Some Point and We Have to Be Ready, NASA Administrator Says He said the reason he was addressing the world's experts on the threat asteroids pose to Earth. Scientists report that significantly fewer asteroids could hit the Earth's surface than previously reckoned. The largest asteroid ever to hit Earth was probably Theia, a Mars-sized body that formed over 4 billion years ago, during the early days of the solar system. An asteroid that big traveling at that speed has the energy roughly equal to a 1 million megaton bomb. Last week, the small 100-meter asteroid 2002 MN was discovered only after it whizzed by the Earth, passing well within the orbit of the Moon. Giotto (retarget) to Comet Grigg-Skellerup. Bennu is a B-type asteroid with a ~500 meter diameter. In 2013, Nasa calculated that Apophis would not hit Earth. At the same time, a few studies have found evidence that the large extinction events on. Scientists turned to craters on the moon for more precise answers about the. If something DOES hit the ground, it is known as a meteorite. which will rendezvous with asteroids and touch. NASA's Near Earth Object Observations Program, of which both Johnson and Fast are a part, has cataloged nearly 900 asteroids around Earth that have a diameter of more than 1 kilometer, or about. What do you think the two craters would look like ten million years in. The Chicxulub crater is the most famous, because it is believed to have wiped out the dinosaurs and allowed mammals to evolve. "Because of this, threatening to hit Earth in 2135. Ideas keep getting put forward, they get kicked around for a while, and they often don’t fare very well,” Asphaug says. The fear of an asteroid similar to the one that hit the earth back then is one reason why tracking asteroids and planetary defence has become a pressing scientific discussion. SHOCK ASTEROID WARNING: Planet earth faces 100 YEARS of killer strikes starting in 2017 ASTEROIDS could rain down on the earth for 100 years, shocked experts have just warned. Usually, asteroids and smaller debris called meteoroids are too small to survive the passage through Earth's atmosphere. " These objects, mostly asteroids, have a chance to hit Earth and cause regional or even global devastation within the next 100 years. Click on the object designation to go to a page with full details on that. The Erythrozyt game is under the collecting games, jumping, obstacle, unity3d, webgl category. Some have orbits that cross Earth's path, and there is evidence that Earth has been hit by asteroids in the past. 1999 KW4 is about 1. Large asteroids have hit Earth dozens of times in the distant past. Asteroids also are fainter the further they get from Earth. The shockwave flattens. Eventually. Studies have predicted that they may hit the Earth on February 1, 2019, and March 16, 2880. It is estimated that an asteroid larger than 10 feet across strikes the Earth around once a year. You can pick a city, enter an address, or just let it hit somewhere at random. Asteroids have been hitting the Earth for billions of years. The impacts would have boiled the oceans, cooked the little dry land, and created a dust cloud locking the Sun for years. Why do comets and asteroids come close to Earth? -Asteroids usually have circular orbits that typically remain between Mars and Jupiter (and close to mars) unless Jupiter knocks the asteroid out of orbit (gravitational PERTURBATION) or the asteroid collides with another asteroid. The Moon acts like an asteroid magnet and has been aggregating asteroids for billions of years. Some have orbits that cross Earth's path, and there is evidence that Earth has been hit by asteroids in the past. The Earth has been getting hit by asteroids and comets for its whole life. There are undoubtedly hundreds of thousands more that are too small to be seen from Earth. It is important to remember that they are just movies and often times do not represent good or true science. It's Unlikely, but a 164-Foot Asteroid May Hit Earth in September. Look at the moon, all the craters that fill its face. These asteroids all have a small but real chance of hitting Earth in the next century Like earthquakes and volcanoes, the most frightening thing about asteroid strikes is their inevitability. From the mysterious Tunguska event to the fossilised Morokweng space rock, when whopper meteorites come along they make a big impact. Ad Free Access to Salon.


text:
1,111,111,111/Mistake/First Edition

Source Work

The Dictionary
$297$

Mistake

So is $1,111,111,111$ [a Kaprekar number ], the smallest Kaprekar number of $10$ digits whose square is $12345678900987654321$.

The square is incorrect. It should be:

$1234567900987654321$

The mistake is not repeated under the section for $1,111,111,111$ itself, in which the square is given correctly.

In Curious and Interesting Numbers, 2nd ed. of $1997$, the number $1,111,111,111^2$ is again given incorrectly in Section $297$, but differently:

$12, 345, 671, 900, 987, 654, 321$

format: plain


text:
## anonymous 3 years ago I have a problem.

1. anonymous

2. anonymous

MathJax Problem

3. anonymous

How to fix it?

4. anonymous

I am using Mozilla Firefox and java script is on.

5. anonymous

Well its something really very diff...

6. anonymous

|dw:1348476792952:dw| etc.

7. mathslover

There is no problem . Can you see this: $$\frac{1}{x-1}-\frac{1}{2x+1}=0$$ Actually that was the problem of the code typed by the user... ` $$and$$ must be inserted at the two ends.

8. anonymous

Thanks @mathslover


text:
# parts of a number

12. it would imply that one manufacturer is acceptable and the other ones aren't, and, The Iranian national classification and codification system known as. It is a common practice to give them sequential dash numbers, or -LH and -RH part number suffixes. Significant part numbering systems are easier to use if you are trying to identify an item through the use of its code inside your company rather than a long description; however, many variations can start to appear when the code is used by other companies, which may be your distributors, and then people can become confused. y For example, if given fixed-point representation is IIII.FFFF, then you can store minimum value is 0000.0001 and maximum value is 9999.9999. Times tables game | Something which is multiplied by something else. This is necessary because of the separation of concerns that often exists in production, in which the maker of each part (whether an in-house department or a vendor) does not have all the information needed to decide whether any particular small variation is acceptable or not (that is, "whether the part will still work" or "whether it will still fit into the assembly" interchangeably). is , the coefficient is A telephone number puts your call straight through to the receiver, like following a street address to someone’s doorstep. , m + In precise typographical and character encoding terms, it is actually a hyphen, not a dash, that is usually used; but the word "dash" is firmly established in the spoken and written usage of the engineering and manufacturing professions; "dash number", not "hyphen number", is the standard term. − y complex number Term: , ) 9 Coefficients We will learn to say, for example, that 6 is the fourth part, or one quarter, of 24, and that 18 is three quarters … por lo menos una muestra en cada una de dichas partes. The area code is the identifier for a geographic region. Did you ever wonder where the digits in your phone number come from, and what they mean? 9 , the coefficient is T are a pair of A telephone number puts your call straight through to the receiver, like following a street address to someone’s doorstep. Draw functions | + The “+1”, or country code is the first thing you dial to reach a phone line anywhere else in the country. With the Counting program you can determine, The attention to detail has resulted in a machine that is user-friendly in. = See the difference between the two expressions in the table below. ) Summary : The imaginary_part function calculates online the imaginary part of a complex number. The “+1”, or country code is the first thing you dial to reach a phone line anywhere else in the country. For example, when referring to a "Hardware, screw, machine, 4-40, 3/4" long,[1] Phillips": The business using such a screw may buy screws from any of those manufacturers, because each supplier manufactures the parts to the same specification. For calculating conjugate of the complex number following z=1+7i, The U.S. government, and most especially its Department of Defense, has standardized various part numbering systems over the decades for it and its suppliers to use, such as the AN (Army-Navy) and MS (Military Standard) hardware classification and numbering systems. is the exponent. 2 ). Award-Winning claim based on CBS Local and Houston Press awards. | Languages available : fr|en|es|pt|de, See intermediate and additional calculations, https://www.solumaths.com/en/math-apps/calc-online/imaginary_part, Calculate online with imaginary_part (imaginary part of complex number), Solving quadratic equation with complex number. is the base, and + ( m Likewise, the integer part of the (real) cubic root of –1729 is To calculate the imaginary part of the following complex expression z=(1+i)/(1-i), You can still create a structure where you can have a category and then a sequential number e.g. Site map cos | cross product calculator | countdown numbers solver | CAS | 9 9 With this function, the calculator allows the online calculation of the imaginary part of a complex number. Differentiation calculator | + Shortcuts : is adopted to deliver the maximum possible mill availability. T "non-intelligent"). 1 7, Product of + {\displaystyle \scriptstyle \left\lceil {\sqrt[{3}]{-1729}}\right\rceil \,=\,-12.\,}, In the OEIS, sequences of nonintegers are sometimes given by their integer parts. Function plotter | (using the formula Factor expression | Simplify expressions calculator | These are different for other countries, but the “1” preceding our numbers is the country code for the United States and Canada. atan | cosine hyperbolic calculator | and Utiliza el Traductor de DeepL para traducir texto y documentos instantáneamente. determinant calculator | − The next grouping is the 3-digit prefix, which narrows the location of the phone number a little further. This concept is helpful in the database management of engineering and production (such as in product data management applications) when it is useful to think of a certain combination of subparts as "one part" (and thus one database record) for ordering, production, or billing purposes. 2 Lesson 15. Division is breaking a number up into an equal number of parts. ; Prefix - The prefix originally referred to the specific switch that a phone line connected to. 3 However, if you would like to try Talkroute’s Virtual Phone System for free, you can sign up for a trial here. 1729 ch calculator | y ( arccos | or it may allow them to involve a range of actors and build on existing local assets. Simplify square root calculator | Simplify fraction calculator | These are the last 4 digits of the phone number which directs a call to a specific phone line. As you probably suspected, each segment has a reason for being there. These suffixes are called dash numbers, and they are a common way of logically associating a set of detail parts or subassemblies that belong to a common assembly or part family.


text:
# Why does X-shooter use double passes through prisms for Echelle cross-dispersion instead of gratings?

The catchy title Down-the-barrel observations of a multiphase quasar outflow at high redshift: VLT/X-shooter spectroscopy of the proximate molecular absorber at z=2.631 towards SDSS J001514+184212 mentions X-shooter (Italian only?) which is described in detail in X-shooter, the new wide band intermediate resolution spectrograph at the ESO Very Large Telescope:

Abstract

X-shooter is the first 2nd generation instrument of the ESO Very Large Telescope (VLT). It is a very efficient, single-target, intermediate-resolution spectrograph that was installed at the Cassegrain focus of UT2 in 2009. The instrument covers, in a single exposure, the spectral range from 300 to 2500 nm. It is designed to maximize the sensitivity in this spectral range through dichroic splitting in three arms with optimized optics, coatings, dispersive elements and detectors. It operates at intermediate spectral resolution (R ~ 4000−17 000, depending on wavelength and slit width) with fixed échelle spectral format (prism cross-dispersers) in the three arms. It includes a 1.8″ × 4″ integral field unit as an alternative to the 11′′ long slits. A dedicated data reduction package delivers fully calibrated two-dimensional and extracted spectra over the full wavelength range. We describe the main characteristics of the instrument and present its performance as measured during commissioning, science verification and the first months of science operations.

To get large dispersion Echelle gratings are operated in high order so you need some kind of cross-dispersion to separate the orders. The one's I've seen use a first-order grating with lines perpendicular to those of the Echelle for cross-dispersion.

X-shooter uses double passes through prisms in each of the three arms of this 300 to 2500 nm single-slit (though there's a 1.8′′×4′′ to 0.6′′×12′′ slicer), single-target spectrograph. For UVB and visible there is one prism, for NIR it's a double pass through three prisms!

The collimated beam passes through a 60° silica prism twice to gain enough cross-dispersion. The main dispersion is achieved through a 180 grooves/mm échelle grating blazed at 41.77°.

The optical layout of the VIS spectrograph is very similar to that of the UVB... For cross-dispersion, it uses a 49° Schott SF6 prism in double pass. The main dispersion is achieved through a 99.4 grooves/mm, 54.0° blaze échelle grating.

(For the) NIR spectrograph... In order to get enough cross dispersion, three prisms are used in double pass. Prism 1 is a 35° top angle made of Infrasil; prisms 2 and 3 are two 22° top angle ZnSe prisms of the largest available thickness (56 mm). This design provides an almost constant order separation. The main dispersion is provided by a 55 grooves/mm échelle grating with a blaze angle of 46.07°.

Question: Why does X-shooter use double passes through prisms for Echelle cross-dispersion instead of gratings? Wouldn't this make it harder to get roughly even order separation?

Dispersion curves ($$n(\lambda)$$) are notoriously nonlinear, they shoot up as you approach short wavelengths were absorption edges happen in the material (ergo Cauchy's $$n(\lambda) \approx A + B/\lambda^2 + C/\lambda^4$$) so prisms squish longer wavelengths and stretch the shorter ones, whereas gratings disperse roughly linearly with wavelength, as $$\Delta sin \theta = \lambda m / d$$. Why the choice of prisms in this case?

Figure 6. shows the NIR spectrograph. "Double pass" means the light passes through the prisms going towards the Echelle and again after being back-diffracted. That's twelve additional optical surfaces!

Figure 6. The NIR spectrograph optical layout.

The light of a celestial object, in this case a quasar, is dispersed according to its wavelength, or colour to form a very long, very high resolution spectrum covering the full wavelength range from ultraviolet to infrared. The optical elements in the spectrograph arrange this long spectrum in a series of consecutive, shorter spectra, called orders. In this illustration, the wavelength increases from bottom to top of each spectrum, and from left to right. The spectrum of the quasar, recording its intensity as a function of the wavelength, is the thin bright lines visible in each of the orders. The short bright nearly horizontal lines correspond to colours where the atmosphere shines brightly.

• Related: How does the ESPRESSO Echelle spectrograph fold the spectrum so nicely? (currently in need of an answer) and in History of Science and Mathematics SE: Where does “the grating equation” come from? Does it have a another name?
– uhoh
Jul 9 '21 at 0:42
• Echelle spectrographs can use either. I think a less specific question might be better. Jul 9 '21 at 7:10
• @ProfRob The question already explains that they can use either, and why it seems to me that gratings would be better. I've asked about a specific instrument because I can read about it and include it as my "prior research". One is welcome to answer broadly why prisms are better or chosen in some cases and explain why this is likely to be one of those cases. But having a good example of heavy use of prisms in the question may make the answer easier as the example is already here.
– uhoh
Jul 9 '21 at 8:01
• The answer may be specific to Xshooter. Jul 9 '21 at 8:19
• @ProfRob then that's good, since that's what I'd like to know!
– uhoh
Jul 9 '21 at 9:08


text:
## Getting started with Riemann

In SupplyFrame we started to use Riemann as our stream processing framework to do system and application monitoring. Riemann is a lightweight clojure based DSL operates on event streams. The power of Clojure expressiveness gives it ability to encode the whole event handling logic into one config file. Compare to generic stream framework like Esper or Storm, it is cleaner, simpler, but still highly programmable.
For example, If we want to send the mean data of last 10 minutes to graphite and alert sysops if the median of metric is more than 1000, we can express the idea in riemann like this:

Pretty clean, right?

### How to install & deploy Riemann

On the homepage of riemann website, there are some prebuilt packages available. You can simply download the deb package and \$ sudo dpkg -i riemann.0.2.x.deb to install it. The package will install the configuration file into /etc/riemann/riemann.config and you can use sudo service riemann start/stop/restart/reload to run or to stop it. If you prefer to use it as an instance instead of a system service, you can clone the project and use leiningen to install the dependencies and compile the project. You can either run Riemann in a screen or use nohup to force it to run as a daemon. If you run Riemann as an instance, remember to assign each Riemann with different ports that it listens to.

### Riemann DSL structure

#### Events

Riemann is designed to operate on flows of events sent over protocol buffers. An event is basically a map of these fields (copied from riemann documentation):

host A hostname, e.g. "api1", "foo.com" e.g. "API port 8000 reqs/sec" Any string less than 255 bytes, e.g. "ok", "warning", "critical" The time of the event, in unix epoch seconds Freeform text Freeform list of strings, e.g. ["rate", "fooproduct", "transient"] A number associated with this event, e.g. the number of reqs/sec. A floating-point time, in seconds, that this event is considered valid for. Expired states may be removed from the index.

You can think that the events in Riemann are nouns, and we're going to use verbs, streams and stream functions to process them.

#### Streams and stream functions

(streams ...) is the magic macro that forms the unique DSL of processing events. The expressions in (streams ...) are treated as rules that process the same event simultaneously; while the nested s-expressions in (streams...) will pipe the results from parent s-expression to child s-expressions.

You can tell from the previous example, (folds/mean ...) and (folds/median ...) are at the same level, which means they're processing the same event. And the event pipeline handling logic is expressed in nested s-expressions.

#### How to handle an event manually 1

Every event handler is a function that takes an event or list of events as input. If you want to deal with an event on the most nested s-expression, its easy. An anonymous function will do the job:

For more example of the basic usage of Riemann and standard stream processing functions, you can find it at Riemann's HOWTO page.

#### How to handle an event manually 2

In most of the use cases, Riemann's built-in stream aggregation functions solve the problems. However, in some rare cases you might also want to write nested stream processing function similar to the built-in functions. Here's how you can do it:

### Case study

Here's an use case. We want to detect errors and those events which exceeds defined threshold. In most alerting systems, they either notify sysops with all peak events or smoothen the data which is even more error prone. We want something like this: in time period if the ratio of overshoot or error events is more than x, pipe the events to handler functions. Here's how we implemented it in Riemann:

With this function, now we can define our event logic as


text:
# Closed Zone

Geometry Level 3

The figure above shows two circles, each with radius 12, goes through each others centers. What is the area of the blue region?

Give your answer to the nearest integer.

×


text:
# Biham-Middleton-Levine traffic model

## An applet of a cellular automaton

### Abstract

The Biham-Middleton-Levin model is a simple system to simulate traffic within a city. It consists of two types of agents (called cars) that can either move down (red) or right (blue). The traffic is controlled by traffic lights, so that in each time step only one type can move. The agent will not move, if it is blocked by an agent of different type or by an agent of the same type which is blocked itself. The system underlies periodic boundary conditions and the characteristics of the system is mainly determined by the density of agents and the random initial conditions. For a low density one will find a free flowing phase (e.g. system size $100$, density $20\%$), where no agent is blocked. For larger densities, a blocked phase (e.g. system size $100$, density $40\%$) is created, so that every agent is blocked. These phases can be observed after a transient period, which is determined by the system size, density and other parameters.
Contents

### Usage of the Applet

In the above applet there are two graphic window, the left one showing the simulation of the agents' movements, the right one depicting the percentage of performed movements per type. For the simulation of the Biham-Middleton-Levine model you can change a few parameters in the applet.
• In the section System Mode one can select the Field mode that provides periodic boundary conditions and corresponds to the original model. The Crossing mode has open boundaries and resembles a crossing of pedestrian crowds. New agents are set to the free fields of the income edge randomly at any time step. (Note: every change initialises a new random initial set.)
• The density of agents is the number of agents (each type about the same number) per area. It determines the behaviour of the system and it can only be changed when the simulation is not running. (Note: every change initialises a new random initial set.) Running the Crossing Field mode however the density slider determines, how many new agents enter the edge of the field.
• With the speed bar one can change the speed of the simulation.
• By car speed you change the relative velocity of the cars. Therefore the red cars (v1) will go on moving one cell per time step, the blue cars will only move with higher velocity (v2). (Note: the agent will only jump in a given time step, when there is enough space infront; e.g. for speed v=3 it needs 3 free fields infront.)
• The system size can be choosen out of four predefined settings. It is the number of cells along an edge of the left field. (Note: every change initialises a new random initial set.)
The usage of the applet should be intuitively. Just try to run the simulation and change some values.
• To start the simulation just choose your prefered settings and press the start button
• To perform only one step of the simulation you can use the arrow button (next to the start button; only works when simulation is not yet running).
• Note: Whenever you change the parameters System Mode, System Size or Density, a new random set will be initialised. These parameters can only be accessed when the simulation is paused.

### Theory

(a) flowing phase system (e.g. system size $100$, density $20\%$)

(b) flowing phase statistics

(c) blocked phase system (e.g. system size $100$, density $40\%$)

(d) blocked phase statistics

With this simulation the authors present three state cellular automaton based on the BML model of Biham, Middleton, and Levine [2]. Cellular automata are a well studied realm in the fields of dynamical systems, and they are often used to simulate traffic. This type of model is much easier and faster to implement than hydrodynamical traffic models. In this section we want to give the theoretical background of the above shown BML model (Field Mode) and describe our extension to the model (Crossing Mode).

BML Model

The set up for the BML model is a $N\times N$ square lattice of which each node can be either occupied by one agent or is empty. There are two different types of agents characterized by the direction of their movement, which can be seen as cars in the streets of a city. Here one type can move only to the right (blue), the other only moves down (red). The initial configuration of agents on the lattice is a random distribution with an total initial agent density $p$ (ratio of number of all agents with the number of available nodes on the lattice), the probability to find an agent of special type is therefore $p/2$.

(e) phase transition (from [2])

The system is constrained to periodic boundary conditions, which forces agents that leave the square on one edge will enter is again on the opposite site. Topologically this makes the square euqivalent to a torus. As described in their paper the dynamics of the system is controlled by traffic lights, so that a single time step only one type of agents will move. The update happens synchronously for all agents of a type. The movement of an agent follows the rule:
• If the node infront (in the direction of movement) is empty, it will go there.
• If the node infront is occupied by an agent of the other type, the agent is blocked.
• If the node infront is occupied by an agent of the same type, the agent will move if the infront agent moves.
In the original system proposed in [2] the speed of the agents is limited to one mode per timestep ($v_1=v_2=1$). In the dynamical behaviour Biham et al. find to different asymptotic states. After a transient period which depends on the initial configuraiton and the system size $N$, the agents are either all moving infinitely long without being blocked (flowing phase) or the agents -- all or only a fraction -- is blocked for ever. In Fig. (a) the system is in the free flowing phase and in the corresponding diagramm in Fig. (b) one can see that after a short time all agents are moving. The blocked phase is depicted in Fig. (c) where the typical diagonal structure can be found. There the different types of agents block another and the diagramm Fig. (d) shows that the number of moving agents goes down to zero.

(f) statistics of an unstable intermediate phase going to a locked phase (e.g. system size $100$, density $30\%$)

In their publication Biham et al. measure the average ensemble velocity after the transient period to describe the system's state. They find that the average velocity depends on the initial density $p$ of agents and that a more or less sharp transition between flowing phase and fully blocked phase can be found. In Fig. (e) this transition is shown for different system sizes. The system state in which only a constant fraction of agents can move is called intermediate phase, and one can clearly see that this intermediate state vanishes for large system size. (Previous investigations have shown that a stable periodic intermediate state can hardly exist on a square lattice. This is more often to be found on a (non-square) rectangular lattice. On a square lattice unstable intermediate state occur close to the critical density, but they always end up in a blocked phase.)
So the transition between the two extreme states becomes very sharp and the critical density $p_c(N)$ where the transition happens, depends on the system size.
In the original publication the authors compare this second order transition to a percolation transition known from network theory. Up to the very day there is no rigorous analysis of this system except for some special cases of very high density.

Extended Pedestrian Model

This mode was introduced by the authors of this applet and is an extension to the original BML model. The main difference is that the system no longer has periodic boundary conditions but open boundaries. The system starts as before with a random initial distribution of agents of density $p_i$ (both types equally often represented) but whenever an agent leaves the field it is gone. On the entrance edge of each agent type, new agents are created randomly with certain probability $p_n$. To give the system the shape of a pedestrian crossing, some areas (black squares) are forbidden areas for the agents. In this way one can simulate the flow of pedestrians on a crossing when showing the behaviour of the BML model. As the boundaries are no more periodic, there won't be any jams, i.e. the fully blocking phase vanishes.

### Code & Documentation

To understand the applet and the way it simulates the given model, the authors share the produced code and a detailled documentation on this.

Available Features
• Documentation of the applet. This documentation was created with help of Javadoc and explains the most important parts of the applet.
• Sourcecode of the Applet. This provides a .zip-file containing all Java-files of the applet.
Java-Sourcecode.
• Class-files of the Applet. If you can not or do not want to compile the applet, this provides a .zip-file containing all .class-files of the applet.
Class-files.

### Acknowledgement, Authors & Contact

Acknowledgement The authors would like to thank the members of the group Prof. C. Gros for the great help when developing this applet. Especially we thank Prof. C. Gros, Rodrigo Echeveste and Bulcsú Sándor for discussing the model, giving good advice for its visualisation and helping to remove all kinds of technical problems.

About the authors Samuel Eckmann is a Bachelor's student in the group of Prof. C. Gros at Goethe University Frankfurt (Main).
Hendrik Wernecke is a Master's student in the group of Prof. C. Gros at Goethe University Frankfurt (Main). He did his Bachelor studies at Ulm University (2010-2013).

Samuel Eckmann
Hendrik Wernecke

[1]
Wikipedia article Biham-Middelton-Levine traffic model
[2]
: Self-organization and a dynamical transition in traffic-flow models, Phys. Rev. A 46, R6124(R), November 1992.
[3]
: Complex and Adaptive Dynamical System - A Primer, Springer-Verlag, 2011.
[4]
: Dynamical traffic light strategy in the Biham-Middleton-Levine model., Physical Review E 87.2 (2013): 022812.
[5]
: Violating traffic light behavior in the Biham-Middleton-Levine traffic flow model, Procedia engineering 31 (2012): 1072-1076.
[6]
: Effect of Car Length in the Biham-Middleton-Levine Traffic Model, Future control and automation. Springer Berlin Heidelberg, 2012. 479-487.
[7]
: Effect of overpasses in the Biham-Middleton-Levine traffic flow model with random and parallel update rule, Physical Review E 88.2 (2013): 022809.

Legal note: We do not take any responsibility for
the content of the webPages linked here-in.


text:
## Friday, 6 May 2011

### 1705 - Nice, nice, nice

It's nice to go out or to stay at home
It's nice to eat and also nice to drink
It's nice to do without or to have some
It's nice to feel complete, but nice wanting
It's nice to speak and also nice to sing
It's nice to be good and nice to be bad
It's nice being dirty, nice to get clean
It's nice to have, even nice being had
It's nice having a mum, nice being dad
It's nice spending, but nice saving income
It's nice to vegetate and nice to think
It's nice to laugh, even nice being sad
It's nice to stand tall and nice to be prone
It's nice to be in the black and the pink


text:
Typesetting with minted
macOS
app.
See other variants:
Windows

minted is a LaTeX package that allows syntax highlighting in your LaTeX source code using the Pygments library. You can read more about it and see some examples at https://github.com/gpoore/minted.

Installing dependencies:

You will need Pygments, the syntax highlighter used by minted. This can be done by running

sudo easy_install Pygments

Shell Escape

minted requires Shell Escape to be enabled. This is a potential security hole and is not enabled by default by Texpad. To enable Shell escape open Preferences, switch to the Typesetting pane and check the -shell-escape box. In Texpad macOS 1.8, minted will be detected by Texpad automatically and a suggestion dialogue will be presented to you to this effect.

Typesetting while hiding intermediate files

By default Texpad invokes LaTeX in such a way that all intermediate files are kept hidden out of sight in the .texpadtmp directory (a hidden directory at the same path as the root file). Unfortunately the minted package requires that this directory must be defined as an option to its \usepackage{minted} command. This may be done by modifying the command to

\usepackage[outputdir=.texpadtmp]{minted}

An alternative is to turn off .texpadtmp. This may be done by opening preferences, choosing the typesetting pane, and unchecking “Hide Intermediate Files”.

An example

This simple example will print the included C++ code with syntax highlighting in your PDF. Note the use of correct options in \usepackage[outputdir=.texpadtmp]{minted} to make minted work with Texpad’s .texpadtmp.

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\end{document}


text:
Cuboid: Definition, Shape, Surface Area, Volume, Formula - Embibe
• Written By Gurudath
• Last Modified 19-07-2022
• Written By Gurudath
• Last Modified 19-07-2022

# Cuboid: Definition, Examples, Formula and Properties

Cuboid Definition: Cuboid shaped objects surround us in our day-to-day life. From television sets, books, carton boxes to bricks, mattresses, and shoeboxes, cuboid objects are all around us. In Geometry, a cuboid is a three-dimensional figure with six rectangular faces, twelve edges, and eight vertices. The cuboid shape comes with a closed three-dimensional figure surrounded by rectangular faces, which are plane regions of rectangles.

This article discusses cuboids, including their definitions and components, like their surface area and volume. Also, we will learn about the net of a cuboid. Read on to find out more.

With Embibe, students can get free CBSE mock tests for all topics. MCQs on Embibe are based on revised CBSE class books, paper patterns, and syllabus for the year 2022. This mock test series has a comprehensive selection of relevant questions and solutions. Candidates in the CBSE board can take these free mock tests to practice and find areas where they need to improve for their board exams.

## What is Cuboid?

Definition: A cuboid is a solid three-dimensional object which has six faces that are rectangular in shape with eight vertices, and twelve edges. Since the cuboid has six faces we can call it a regular hexahedron.

### Examples of Cuboid

The textbooks we read, the lunch boxes we bring to school, the mattresses we sleep on and the bricks we use to build a house, and many other things, are well-known examples of cuboids in our environment.

### How Does a Cuboid Look?

As discussed earlier, the cuboid has $${\rm{6}}$$ faces, $${\rm{8}}$$ vertices, and $${\rm{12}}$$ edges.

In solid geometry, any $${\rm{3}}$$-dimensional figure has length, breadth, and height.

Let’s first learn about the basic parameters like face, vertex, and edge which play an important role in $${\rm{3}}$$-dimensional objects.

Faces: Any of the individual flat surfaces of a solid object is known as the face of that object.

Vertex: In a $${\rm{3}}$$-dimensional object, a point where two or more lines meet is known as a vertex. Also, a corner can also be referred to as a vertex.

Edge: An edge is a line segment joining two vertices.

So, now let us try to imagine a cuboid with the above-said parameters. The shape of the cuboid appears to be as follows:

In the figure below, $${\rm{l,}}\,{\rm{b}}$$ and $${\rm{h}}$$ stand for length, breadth or width, and height respectively of the cuboid.

Solid geometry is associated with $${\rm{3 – D}}$$ shapes and figures with surface areas and volumes.

Now, let us learn about the surface area and volume of a cuboid.

## Cuboid Formula

Let us look at some of the formulas for cuboid:

### Surface Area of Cuboid

We know that, area can be defined as the space enclosed by a flat shape or the surface of an object. The area of a figure is the number of unit squares that enfold the surface of a closed figure.

Similarly, the total surface area of a solid is the sum of the areas of the total number of faces or surfaces of the solid.

The lateral surface area of a solid is the surface area of the solid excluding the top and base.

Now, let us find out the total surface area and a lateral surface area of a cuboid.

We have said that the cuboid has six rectangular faces.

In the above figure, let $${\rm{l}}$$ be the length, $${\rm{b}}$$ be the breadth, and $${\rm{h}}$$ be the height of a cuboid.

Therefore, $$AD = BC = GF = HE = l$$
$$AB = CD = GH = FE = b$$
$$CF = DE = BG = AH = h$$

Now, the lateral surface area of the cuboid $$=$$ Area of rectangular face $$ABGH +$$ Area of rectangular face $$DCEF +$$ Area of rectangular face $$ADEH +$$ Area of rectangular face $$BCGF$$

$$= \left( {AB \times BG} \right) + \left( {DC \times CF} \right) + \left( {AD \times DE} \right) + \left( {BC \times CF} \right)$$

$$= \left( {b \times h} \right) + \left( {b \times h} \right) + \left( {l \times h} \right) + \left( {l \times h} \right)$$

$$= 2\left( {b \times h} \right) + 2\left( {l \times h} \right)$$
$$= 2\,h\left( {l + b} \right)$$

Therefore, lateral surface area of a cuboid $$= 2h\left( {l + b} \right)\,{\rm{sq}}{\rm{.units}}$$

Now, the total surface area of a cuboid is the sum of the areas of a total number of faces or surfaces that include the cuboid. The faces include the top and bottom (bases) and the remaining surfaces.

Area of face $$ABCD =$$ Area of face $$EFGH = \left( {l \times b} \right)$$
Area of face $$CDEF =$$ Area of face $$ABGH = \left( {b \times h} \right)$$
Area of face $$BGCF =$$ Area of face $$ADHE = \left( {l \times h} \right)$$
$$=$$Area of $$\left( {ABCD + EFGH + CDEF + ABGH + BGCF + ADHE} \right)$$
$$= \left( {l \times b} \right) + \left( {l \times b} \right) + \left( {b \times h} \right) + \left( {b \times h} \right) + \left( {l \times h} \right) + \left( {l \times h} \right)$$
$$= 2\left( {l \times b} \right) + 2\left( {b \times h} \right) + 2\left( {l \times h} \right)$$
$$= 2\left( {lb \times bh \times lh} \right)$$

### Volume of a Cuboid

Volume is the amount of $$3$$-dimensional space occupied by a solid object, such as the space occupied or contained by a substance (solid, liquid, gas, or plasma). Volume is often measured numerically using the SI-derived unit, the cubic meter $${{\text{m}}^3}$$.

So, volume $${\rm{ = }}\left( {{\rm{Length \times Breadth \times Height}}} \right)$$ $$= l \times b \times h$$
Therefore, the volume of a cuboid $$= lbh$$

### Perimeter of a Cuboid

Perimeter is the sum of lengths of all the edges of a cuboid.
From the above figure, we know that,
$$AD = BC = GF = HE = l$$
$$AB = CD = GH = FE = b$$
$$CF = DE = BG = AH = h$$
So, perimeter of a cuboid $$= AD + BC + GF + HE + AB + CD + GH + FE + CF + DE + BG + AH$$
$$= \left( {l + l + l + l} \right) + \left( {b + b + b + b} \right) + \left( {h + h + h + h} \right)$$
$$= 4\left( {l + b + h} \right)$$
Therefore, the perimeter of a cuboid $$= 4\left( {l + b + h} \right)$$

### Formula to Find Length of the Diagonal of a Cuboid

The formula to find the length of the diagonal of a cuboid is given by $$\sqrt {{l^2} + {b^2} + {h^2}} .$$

## What are Nets?

1. A geometry net is a two-dimensional shape that can be folded to form a $$3$$-dimensional shape or a solid.
2. A net is a pattern made when the surface of a three-dimensional figure is put forward flat showing each face of the figure.
3. A solid may have different nets.

### How Many Nets of Cuboid are There?

A cuboid can be drawn in $$54$$ different nets of three different lengths.
One of them is shown below:

### Properties of a Cuboid

Let us look at some of the properties of a cuboid:

1. A cuboid has $$6$$ rectangular faces.
2. A cuboid has $$8$$ corner points which are known as vertices.
3. A cuboid has $$12$$ line segments joining two vertices known as edges.
4. All angles in a cuboid are right angles
5. The edges opposite to each other are parallel.

### Solved Examples – Cuboid

Let us look at some of the solved examples for cuboid:

Question 1: Find the total surface area (TSA) of a cuboid whose length, breadth, and height are $${\rm{6}}\,{\rm{cm,}}\,{\rm{4}}\,{\rm{cm}}$$ and $${\rm{2}}\,{\rm{cm}}$$ respectively.
Answer: Given: $$l = 6\,{\rm{cm}},\,b = 4\,{\rm{cm}}$$ and $$h = 2\,{\rm{cm}}$$
We know that the total surface area of a cuboid is $$2\left( {lb + bh + lh} \right)$$
So, the total surface area of the given cuboid $$= 2\left[ {\left( {6 \times 4} \right) + \left( {4 \times 2} \right) + \left( {2 \times 6} \right)} \right]{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$${\rm{ = 2}}\left[ {{\rm{24 + 8 + 12}}} \right]{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$${\rm{ = 2}}\left( {{\rm{44}}} \right)\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$${\rm{ = 88}}\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
Therefore, the total surface area of cuboid $${\rm{ = 88}}\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$

Question 2: Find the total surface area of the following cuboid whose length, breadth and height are $${\rm{4}}\,{\rm{cm,}}\,{\rm{4}}\,{\rm{cm}}$$ and $${\rm{10}}\,{\rm{cm}}$$ respectively.
Answer: Given: $$l = 4\,{\rm{cm}},\,b = 4\,{\rm{cm}}$$ and $$h = 10\,{\rm{cm}}$$
We know that the total surface area of a cuboid is $$2\left( {lb + bh + lh} \right).$$
So, the total surface area of the given cuboid $$= 2\left[ {\left( {4 \times 4} \right) + \left( {4 \times 10} \right) + \left( {4 \times 10} \right)} \right]{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$$= 2\left[ {16 + 40 + 40} \right]{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$$= 2\left( {96} \right){\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$${\rm{ = 192}}\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
Therefore, the total surface area of cuboid $${\rm{ = 192}}\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$

Question 3: Calculate the lateral surface area of a cuboid of dimensions $${\rm{10}}\,{\rm{cm \times 6}}\,{\rm{cm \times 5}}\,{\rm{cm}}{\rm{.}}$$
Answer: Given: $$l = 10\,{\rm{cm}},\,b = 6\,{\rm{cm}}$$ and $$h = 5\,{\rm{cm}}$$
We know that the lateral surface area of a cuboid is $$2h\left( {l + b} \right)$$ $${\text{sq}}{\text{.units}}$$
So, LSA of the given cuboid $$= 2 \times 5\left( {10 + 6} \right)$$
$$= 10\left( {16} \right)\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
$$= 160\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$
Therefore, LSA of the given Cuboid $$= 160\,{\rm{c}}{{\rm{m}}^{\rm{2}}}$$

Question 4: Find the length of the longest pole that can be put in a room of dimensions $${\rm{10}}\,{\rm{m \times 10}}\,{\rm{m \times 5}}\,{\rm{m}}$$
Answer: Given: $$l = 10\,{\rm{m}},\,b = 10\,{\rm{m}}$$ and $$h = 5\,{\rm{m}}$$
Length of the longest pole $$=$$ Diagonal of a Cuboid (room)
We know that the diagonal of a Room $$= \sqrt {{l^2} + {b^2} + {h^2}}$$
$$= \sqrt {{{10}^2} + {{10}^2} + {5^2}} {\rm{m}}$$
$$= \sqrt {100 + 100 + 25} \,{\rm{m}}$$
$$= 225\,{\rm{m}}$$
$$= 15\,{\rm{m}}$$
Therefore, the length of the longest pole is $$= 15\,{\rm{m}}{\rm{.}}$$

Question 5: A cuboid has dimensions $$60\;{\rm{cm}} \times 54\,{\rm{cm}} \times 30\,{\rm{cm}}.$$ Find the Volume of a cuboid.
Answer: Given: $$l = 60\,{\rm{cm}},\,b = 54\,{\rm{cm}}$$ and $$h = 30\,{\rm{cm}}$$
We know that the volume of a cuboid $$= l \times b \times h$$
$$= \left( {60 \times 54 \times 30} \right){\rm{c}}{{\rm{m}}^{\rm{3}}}$$
$$= 97200\,{\rm{c}}{{\rm{m}}^{\rm{3}}}$$
Therefore, the volume of a cuboid $$= 97200\,{\rm{c}}{{\rm{m}}^{\rm{3}}}$$

### Summary About Shape of Cuboid

From the above article, we learn how to define a cuboid, an example of a cuboid and what is the number of faces, edges and vertices of a cuboid. Also, we hope that we have helped you to learn how to find the volume and surface area of the cuboid with the given measures.

Also Check,

### Frequently Asked Questions About Cuboid

Q.1. Do cuboids have square faces?
Ans: Yes, a cuboid can have a square face. The cuboid is a solid $$3$$-dimensional object having $$12$$ rectangular faces. If any two faces of a cuboid are square, then it is called a square cuboid.
Example: Square Prism.

Q.2. Can a cuboid have all rectangular faces?
Ans: Yes, the cuboid is a solid $$3$$-dimensional object having $$12$$ rectangular faces.

Q.3. What is the cuboid formula?
Ans: The formula to find the various parameters of a cuboid is given below.
The total surface area of a cuboid is $$2\left( {lb + bh + lh} \right)\,{\rm{sq}}{\rm{.units}}$$
The Lateral surface area of a cuboid is $$2\left( {lb + bh + lh} \right)\,{\rm{sq}}{\rm{.units}}$$
The length of a diagonal of a cuboid $$= \sqrt {{l^2} + {b^2} + {h^2}}$$
The volume of a cuboid $$= l \times b \times h\,{\rm{cubic}}\,{\rm{units}}$$
The perimeter of a cuboid $$= 4\left( {l + b + h} \right)$$

Practice Cuboid Questions with Hints & Solutions


text:
# Klein Four Group

• Feb 21st 2010, 10:50 AM
nmatthies1
Klein Four Group
Let G be a Klein Four Group. How many distinct homomorphisms $\phi : G \to G$ are there? How many of these are isomorphisms?

Stuck on how to start this. Any hints?
• Feb 21st 2010, 11:18 AM
tonio
Quote:

Originally Posted by nmatthies1
Let G be a Klein Four Group. How many distinct homomorphisms $\phi : G \to G$ are there? How many of these are isomorphisms?

Stuck on how to start this. Any hints?

Write $G=\{1,a,b,ab\}=$ . Now, any endomorphism of $G$ is uniquely determined by its values on the generators $a,b$...now start from here.

Tonio
• Feb 22nd 2010, 01:04 AM
nmatthies1
I don't understand...What exactly do you mean by "is uniquely determined by its values on the generators http://www.mathhelpforum.com/math-he...09167892-1.gif, ..." ?
• Feb 22nd 2010, 01:57 AM
HallsofIvy
The Klein four group has two generators, a and b. Any homomophism must map generators to generators- it must map {a, b} into itself- or map one or more generators onto the identity (I added this last part- I think we need to include this). Any isomorphism must map the set of generators one-to-one and onto itself.
• Feb 22nd 2010, 02:05 AM
tonio
Quote:

Originally Posted by HallsofIvy
The Klein four group has two generators, a and b. Any homomophism must map generators to generators- it must map {a, b} into itself- or map one or more generators onto the identity (I added this last part- I think we need to include this). Any isomorphism must map the set of generators one-to-one and onto itself.

I think there is some confusion here: any HOMOMORPHISM from G to itself (i.e., an endomorphism of G) is uniquely determined by its action on any set of generators of G, but it doesn't HAVE TO map generators to generators. It can map a generator to an element whose order is a divisor of the generator's one, for example.

Now, an ISOMORPHISM from G to G (i.e., an automorphism of G) has to map generators to generators.

So, for example, the map $f(a)=b,\, f(b)=1,\,f(ab)=b,\,f(1)=1$ is an endomorphism of G but not an automorphism (why?), whereas the map $g(a)=ab,\,g(b)=a,\,g(ab)=b,\,g(1)=1$ is an automorphism of G(why?)

Tonio
• Feb 22nd 2010, 03:34 AM
Topologist
Description of the endomorphisms of the Klein group
Quote:

Originally Posted by nmatthies1
I don't understand...What exactly do you mean by "is uniquely determined by its values on the generators http://www.mathhelpforum.com/math-he...09167892-1.gif, ..." ?

Let us denote the Klein group by $G=\{e,a,b,c\}$, where e is the identity of G and a, b and c are the three elements of order 2 in G. Intuitively, we cannot "distinguish" between a, b and c in a group-theoretic manner; notice that $a^2=b^2=c^2=e$, that $ab=ba=c$, that $ac=ca=b$, and that $bc=cb=a$. In some sense, therefore, there is a "symmetry" between the elements a, b and c.Mathematically, we say that there is an isomorphism of G that carries a to b, an isomorphism that carries a to c, an isomorphism that carries b to c; succintly, every permutation of a, b and c corresponds to an isomorphism of G. Therefore, there are precisely 6 isomorphisms from G to G, since there are precisely 6 permutations on three letters.

How do we determine the number of homomorphisms from G to G? Well, we can consider the kernel of each homomorphism in doing so (recall the first isomorphism theorem?). Since G is abelian, every subgroup of G is normal, and therefore a kernel for some homomorphism defined on G. However, if we deal exclusively with non-trivial homomorphisms that are not isomorphisms, the only possibilities for the kernel of the given homomorphism are $K_1=\{e,a\}$, $K_2=\{e,b\}$ and $K_3=\{e,c\}$. By the first isomorphism theorem, $|\mbox{Im}(f)|=\frac{|G|}{|\mbox{Ker}(f)|}$, and therefore whether the kernel of f is $K_1$, $K_2$ or $K_3$, the image of f must be a subgroup of order 2. Since there are 3 subgroups of G of order 2, and three posibilities for the kernel of f, there are precisely 9 homomorphisms from G to G that are non-trivial and not isomorphisms. Since we discovered that there are 6 isomorphisms of G earlier (and of course there is one trivial homomorphism of G mapping every element of G to the identity), there are in total 16 isomorphisms of G.

Does this answer your questions? Regarding the idea that a homomorphism is "uniquely determined by its values on the generators of its domain", recall that if C is a cyclic group and f is a homomorphism on C, f is determined by its image of the generator of C. Why? If g generates C, and $f(g)=x$ (for some x in the range of f), $f(g^i)=[f(g)]^i=x^i$. Since every element of C is a power of g by the very definition of cyclic groups, the image of every element of C under f is determined by the image of the generator of C under f. Essentially, this idea generalizes to groups with more than one generator; it might be a good exercise to appreciate this thoroughly.
• Feb 25th 2010, 10:53 PM
nmatthies1
Thank you! Will go through your posts in more detail over the weekend to see if I fully understand it.
• Mar 31st 2011, 05:07 PM
mulaosmanovicben
Quote:

Originally Posted by tonio
I think there is some confusion here: any HOMOMORPHISM from G to itself (i.e., an endomorphism of G) is uniquely determined by its action on any set of generators of G, but it doesn't HAVE TO map generators to generators. It can map a generator to an element whose order is a divisor of the generator's one, for example.

Now, an ISOMORPHISM from G to G (i.e., an automorphism of G) has to map generators to generators.

So, for example, the map $f(a)=b,\, f(b)=1,\,f(ab)=b,\,f(1)=1$ is an endomorphism of G but not an automorphism (why?), whereas the map $g(a)=ab,\,g(b)=a,\,g(ab)=b,\,g(1)=1$ is an automorphism of G(why?)

Tonio

if an isomorphism maps generators to generators how could f(a)=ab allow f to be an isomorphism?

So far I have this:

Since an endomorphism is uniquely defined by the actions on its generators. And for the klein 4 group the generators are a and b then There are 3 choices for a and 2 choices for b so there are 6 endomorphisms? This does not seem right. Could you guys help me out?
• Mar 31st 2011, 07:22 PM
Deveno
a homomorphism φ is completely determined by its image on two of the elements of order 2 in G. let's call them a and b, its as good as any other names. so how many ways can we pick a 2-element set out of a 4-element set? 2^4 = 16 ways. 6 of these mappings are automorphisms (that take generators to distinct generators, one of which is the identity map on G).

that map that takes a-->1 b-->1 results in everything going to 1, the trivial map. that leaves 9 other possible homomorphisms.

suppose a-->1. since we have already counted the trivial map, we have 3 choices for the image of b. these map {1,a,b,ab} to {1,φ(b)} with kerφ = {1,a}.

similarly b-->1 yields 3 homomorphisms with {1,a,b,ab} going to {1,φ(a)} with kerφ = {1,b}.

so, what's left? well, the only possibilities are that a and b go to the SAME generator of G, (3 choices here) and we have kerφ = {1,ab}.

that is, all 16 maps of {a,b} to G yield homomorphisms. and these must be the ONLY homomorphisms because φ(1) has to be 1, and φ(ab) has to be φ(a)φ(b).
• Apr 1st 2011, 04:37 AM
Swlabr
Quote:

Originally Posted by mulaosmanovicben
if an isomorphism maps generators to generators how could f(a)=ab allow f to be an isomorphism?

So far I have this:

Since an endomorphism is uniquely defined by the actions on its generators. And for the klein 4 group the generators are a and b then There are 3 choices for a and 2 choices for b so there are 6 endomorphisms? This does not seem right. Could you guys help me out?

Because $ab$ is a generator! $\langle a, ab\rangle = \langle ab, b\rangle = \langle a, b\rangle$. Indeed, HallsOfIvy's claims that the Klein 4-group has 2 generators is incorrect! It has 3! But it can be generated by 2. That is, you need to work out where a and b are sent, but they can also be sent to ab!

However, I believe you have all the information you need to continue on your own. I mean, in the example Tonio gave you can notice/work out that the function is a homomorphism, and that it is an injection (trivial kernel) and a surjection, and so it is an automorphism!


text:
### Home > CCG > Chapter 5 > Lesson 5.1.4 > Problem5-43

5-43.

Write an equation for each sequence.

1. $108$, $120$, $132$, $\dots$

A recursive formula specifies the first term, then gives a formula for each 'next term' based on the previous term.

Identify the first term and common difference in the sequence.

$a_1=\text{starting value}$; $a_n=a_{n-1}+d$, where $a_{n-1}$ stands for previous term and $d$ stands for the difference in the sequence.

$a_1=108$; $a_n=a_{n-1}+12$

1. $\frac { 2 } { 5 }$, $\frac { 4 } { 5 }$, $\frac { 8 } { 5 }$, $\dots$

Find the pattern in the sequence. What do you have to multiply by in order to get to the next term?

$a_1=\text{starting value}$; $a_n=(a_{n-1})(r)$, where $a_{n-1}$ stands for the previous term and "$r$" stands for the the common ratio (multiplier) in the sequence

$a_1=\frac{2}{5}$$a_n=(a_{n-1})(2)$

1. $3741$, $3702$, $3663$, $\dots$

The general equation for an arithmetic sequence is $a(n)=d(n-1)+a_1$, where $n=\text{position}$ in the sequence, $d$ is the difference, and $a_1$ is the starting value.

$a(n)=39(n-1)+3741$

1. $117$, $23.4$, $4.68$, $\dots$

Find the common ratio (multiplier) in the sequence.

Use the equation for geometric sequences:

$a_n=a_1·r^{n-1}$

$a_n=117(0.2)^{n-1}=585(0.2)^n$


text:
On problems 3 and 4 find the radius of convergence and the interval of

# On problems 3 and 4 find the radius of convergence

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Justify your answer.
_________________________________________________________________________________________ On problems 3 and 4, find the radiusof convergence and the intervalof convergence. Show all work.3. 1127nnnnxnRadius = __________Interval = ______________________________________________________________________________________________________________4. 0232!nnnxnRadius = __________Interval = ____________________5. Let fbe the function given by sin33fxx, and let P xbe the third-degree Taylorpolynomial for fabout x= 0.(a) Find P x(b) Use the Lagrange error bound to show that 111222fP 2 . .
__________________________________________________________________________________________ 6. Find a power series for 14xfxxcentered at x= 0. Write the first four nonzero termsand the general term. 2 __________________________________________________________________________________________ 7. If fis a function such that sincos ,fxxxfind the coefficient of the 6xterm in the Taylor series for fxabout x= 0.8. The Maclaurin series for fxis given by 2462011...2!4!6!8!22 !nnnxxxxn.(a) Find 40 .(b) Determine whether f has a relative maximum, relative minimum, or neither at x= 0. Justify your answer.(c) Give the exact value for f(1) f __________________________________________________________________________________________ 9. The Maclaurin series for the function fis given by 12340248162...2341nnxxxxfxxn.(a) Write the first four nonzero terms and the general term for the Maclaurin series for fx(b) Use the Maclaurin series you found in (a) to approximate the value of 14f accurate to .01 .

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• Summer '16


text:
Deals Of The Week - hours only!Up to 80% off on all courses and bundles.-Close
Introduction
Concatenation
Simple text functions
12. Functions lower, upper, initcap – usage
How to modify strings
Review

Instruction

Fine! The three functions we've just gotten to know: lower(), upper() and initcap() can also be used to find some data, even if we're not sure about the letters' cases. This often happens when we work with data provided by our users, which are often messy: one person will use capital letters only, another one will use lower case, yet another will provide letters in a random case. Or another problem: we've got an item called riVer Flow for which we want to find the id, but we may not remember which letters were written with lower and upper case. What to do then? Take a look:

SELECT id
FROM item
WHERE lower(name) = 'river flow';

Smart, isn't it? Whatever the case of the name, we can simply put it in lower case and then compare it with 'river flow'. Of course, you could use upper(name)='RIVER FLOW' or initcap(name)='River Flow' just as well.

By the way, this trick could be very useful if you had a chaotic database, with some column values written in lowercase letters only, others with an initial capital letter, and so on. Data aren't always consistent across all rows, so keep these functions in mind.

Exercise

Show the id of the item whose name written in upper case is TRIPCARE.

Stuck? Here's a hint!

In the WHERE clause, use upper(name)='TRIPCARE'.


text:
1. i am trying to push myself and learn these furTher exercises in my maths i would any appreciate any comments and help.

Question 1 what is probability u happens if n happens... P(U INTERSECTION N) / P(U)?

Question 2 probability of U or S happening in the sample space of UDP or 52 byte size packet? Let me think hmmm
450,000: UDP, 20% UDP 450,000 times 0.2 answr correct??

Question 3 pick at random packet and packet of size 52. 1million packet so (0.2*450,000)+(0.9*500,000) correct again?

Question 4 probabalility u happens given s happens and is type of UDP ok P(U intersection S) / P(U)?

Question 5 not of size 52 bytes and is UDP so probability of U given N oh ok.
P(U intersection N) / P(N) = (450,000 INTERSECTION (450,000 * 0.8)) / (450000*0.8+500,000 * 0.1)???
Sample size of anything is equal to 1.

Nevertheless i am not quite sure i am appreciating insight and help, thanks.

2. Originally Posted by Leanna
i am trying to push myself and learn these furTher exercises in my maths i would any appreciate any comments and help.

Question 1 what is probability u happens if n happens... P(U INTERSECTION N) / P(U)?

Question 2 probability of U or S happening in the sample space of UDP or 52 byte size packet? Let me think hmmm
450,000: UDP, 20% UDP 450,000 times 0.2 answr correct??

Question 3 pick at random packet and packet of size 52. 1million packet so (0.2*450,000)+(0.9*500,000) correct again?

Question 4 probabalility u happens given s happens and is type of UDP ok P(U intersection S) / P(U)?

Question 5 not of size 52 bytes and is UDP so probability of U given N oh ok.
P(U intersection N) / P(N) = (450,000 INTERSECTION (450,000 * 0.8)) / (450000*0.8+500,000 * 0.1)???
Sample size of anything is equal to 1.

Nevertheless i am not quite sure i am appreciating insight and help, thanks.
Hi Leanna,

Welcome to MHB!

Let me see if I can try to help some...

Quote:
Question 1 what is probability u happens if n happens... P(U INTERSECTION N) / P(U)?
Here is what you correctly stated : $\displaystyle P(U|N) = \frac{P(U \cap N)}{P(N)}$.

This is a question on Bayes' Theorem. Usually we can rewrite the above in an equivalent way:

$\displaystyle P(U|N) = \frac{P(U \cap N)}{P(N)} = \frac{P(N|U)\cdot P(U)}{P(N)}$

Looking at this it makes sense that the first question written on the page is $P(N|U)$. Do you have any idea what this probability is?

P(n|u) = 0.8 right?
P(n|t) = 0.1 right ? and

4. Originally Posted by Leanna
P(n|u) = 0.8 right?
P(n|t) = 0.1 right ? and
Yes these both sound correct to me.

To finish answering your first question, what is $P(U)$ and what is $P(N)$ (this one is trickier)?

Originally Posted by Jameson
Yes these both sound correct to me.

To finish answering your first question, what is $P(U)$ and what is $P(N)$ (this one is trickier)?
I worked that out but is the last question 0.667 (3d.p), the reason I'm not sure about this last question is because the approximations at the bottom is different.

And is the second to last question I think: $P(U|S)$ = (90,000/1,000,000) / (540,000/1,000,000)
Only these two I'm not completely sure it's right, what do you think? 😁

6. Originally Posted by Leanna
I worked that out but is the last question 0.667 (3d.p), the reason I'm not sure about this last question is because the approximations at the bottom is different.

And is the second to last question I think: $P(U|S)$ = (90,000/1,000,000) / (540,000/1,000,000)
Only these two I'm not completely sure it's right, what do you think? 😁
$\displaystyle P(U|S) = \frac{P(S|U)\cdot P(U)}{P(S)}$

The numerator has two components to multiply and $P(S)$ can be expanded into two cases using the . $P(S)=P(S|U)\cdot P(U)+P(S|T)\cdot P(T)$.