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David P. Robbins
David Peter Robbins (12 August 1942 in Brooklyn – 4 September 2003 in Princeton) was an American mathematician. He is most famous for introducing alternating sign matrices.. He is also known for his work on generalizations of Heron's formula on the area of polygons, due to which Robbins pentagons ( cyclic pentagons with integer side lengths and areas) were named after him. Robbins grew up in Manhattan, where he attended the Fieldston School. He studied at Harvard, where his undergraduate advisor was Andrew Gleason. He went to MIT to do his graduate work and, after a hiatus during which he taught at Fieldston, finished his Ph.D. in 1970. He then taught at MIT, Phillips Exeter Academy, Hamilton College and Washington and Lee University. In 1980 he moved to Princeton, New Jersey and worked at the Institute for Defense Analyses Center for Communications Research there until his death from pancreatic cancer. A symposium was held in Robbins' honor in June 2003, the papers fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brooklyn
Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelve original counties established under English rule in 1683 in what was then the Province of New York. As of the 2020 United States census, the population stood at 2,736,074, making it the most populous of the five boroughs of New York City, and the most populous Administrative divisions of New York (state)#County, county in the state.Table 2: Population, Land Area, and Population Density by County, New York State - 2020 New York State Department of Health. Accessed January 2, 2024. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pancreatic Cancer
Pancreatic cancer arises when cell (biology), cells in the pancreas, a glandular organ behind the stomach, begin to multiply out of control and form a Neoplasm, mass. These cancerous cells have the malignant, ability to invade other parts of the body. A number of types of pancreatic cancer are known. The most common, pancreatic adenocarcinoma, accounts for about 90% of cases, and the term "pancreatic cancer" is sometimes used to refer only to that type. These adenocarcinomas start within the part of the pancreas that makes digestive enzymes. Several other types of cancer, which collectively represent the majority of the non-adenocarcinomas, can also arise from these cells. About 1–2% of cases of pancreatic cancer are neuroendocrine tumors, which arise from the hormone-producing neuroendocrine cell, cells of the pancreas. These are generally less aggressive than pancreatic adenocarcinoma. Signs and symptoms of the most-common form of pancreatic cancer may include jaundice, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2003 Deaths
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked below. 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 Earlier years ''Deaths in years earlier than this can usually be found in the main articles of the years.'' See also * Lists of deaths by day * Deaths by year (category) {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1942 Births
The Uppsala Conflict Data Program project estimates this to be the deadliest year in human history in terms of conflict deaths, placing the death toll at 4.62 million. However, the Correlates of War estimates that the prior year, 1941, was the deadliest such year. Death toll estimates for both 1941 and 1942 range from 2.28 to 7.71 million each. Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: The Declaration by United Nations is signed by China, the United Kingdom, the United States, the Soviet Union, and 22 other nations, in which they agree "not to make any separate peace with the Axis powers". * January 5 – WWII: Two prisoners, British officer Airey Neave and Dutch officer Anthony Luteyn, escape from Colditz Castle in Germany. After travelling for three days, they reach the Swiss border. * January 7 – WWII: ** Battle of Slim River: Japanese forces of the 5th Division (Imperial Japanese Army), 5th Division, sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Cube
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.. See in particulap. 671. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.. Unit hypercube The term ''unit cube'' or unit hypercube is also used for hypercubes, or "cubes" in ''n''-dimensional spaces, for values of ''n'' other than 3 and edge length 1. Sometimes the term "unit cube" refers in specific to the set , 1sup>''n'' of all ''n''-tuples of numbers in the interval , 1 The length of the longest diagonal of a unit hypercube of ''n'' dimensions is \sqrt n, the square root of ''n'' and the (Euclidean) length of the vector (1,1,1,....1,1) in ''n''-dimensional space. See also * Doubling the cube * ''k''-cell * Robbins constant, the average distance between two random points in a unit cube * Tychonoff cube, an infinite-dimensional analogue of the unit cube *Unit square *Unit sphere In mathematics, a unit sphere is a sph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robbins Constant
In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen. Even for simple shapes such as a square or a triangle, solving for the exact value of their mean line segment lengths can be difficult because their closed-form expressions can get quite complicated. As an example, consider the following question: : ''What is the average distance between two randomly chosen points inside a square with side length 1?'' While the question may seem simple, it has a fairly complicated answer; the exact value for this is \frac. Formal definition The mean line segment length for an ''n''- dimensional shape ''S'' may formally be defined as the expected Euclidean distance , , ⋅, , between two random points ''x'' and ''y'', : \mathbb E x-y\, \frac1\int_S \int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler Conjecture
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is around 74.05%. In 1998, the American mathematician Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales' proof, and the Kepler conjecture was accepted as a theorem. In 2014, the Flyspeck project team, headed by Hales, announced the completion of a formal proof of the Kepler conjecture using a combination of the Isabelle a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas C
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Idaho * Thomas, Illinois * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts and entertainment *Thomas (Burton novel), ''Thomas'' (Burton novel) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samuel P
Samuel is a figure who, in the narratives of the Hebrew Bible, plays a key role in the transition from the biblical judges to the United Kingdom of Israel under Saul, and again in the monarchy's transition from Saul to David. He is venerated as a prophet in Judaism, Christianity, and Islam. In addition to his role in the Bible, Samuel is mentioned in Jewish rabbinical literature, in the Christian New Testament, and in the second chapter of the Quran (although the text does not mention him by name). He is also treated in the fifth through seventh books of ''Antiquities of the Jews'', written by the Jewish scholar Josephus in the first century. He is first called "the Seer" in 1 Samuel 9:9. Biblical account Family Samuel's mother was Hannah and his father was Elkanah. Elkanah lived at Ramathaim in the district of Zuph. His genealogy is also found in a pedigree of the Kohathites (1 Chronicles 6:3–15) and in that of Heman the Ezrahite, apparently his grandson (1 Chronicles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David P
David (; , "beloved one") was a king of ancient Israel and Judah and the third king of the United Monarchy, according to the Hebrew Bible and Old Testament. The Tel Dan stele, an Aramaic-inscribed stone erected by a king of Aram-Damascus in the late 9th/early 8th centuries BCE to commemorate a victory over two enemy kings, contains the phrase (), which is translated as " House of David" by most scholars. The Mesha Stele, erected by King Mesha of Moab in the 9th century BCE, may also refer to the "House of David", although this is disputed. According to Jewish works such as the '' Seder Olam Rabbah'', '' Seder Olam Zutta'', and ''Sefer ha-Qabbalah'' (all written over a thousand years later), David ascended the throne as the king of Judah in 885 BCE. Apart from this, all that is known of David comes from biblical literature, the historicity of which has been extensively challenged,Writing and Rewriting the Story of Solomon in Ancient Israel; by Isaac Kalimi; page 32; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over concerns about competing with the '' American Journal of Mathematics''. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
