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Hadwiger–Nelson Problem
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distance 1 from each other have the same color. The answer is unknown, but has been narrowed down to one of the numbers 5, 6 or 7. The correct value may depend on the choice of axioms for set theory. Relation to finite graphs The question can be phrased in graph theoretic terms as follows. Let ''G'' be the unit distance graph of the plane: an infinite graph with all points of the plane as vertices and with an edge between two vertices if and only if the distance between the two points is 1. The Hadwiger–Nelson problem is to find the chromatic number of ''G''. As a consequence, the problem is often called "finding the chromatic number of the plane". By the de Bruijn–Erdős theorem, a result of , the problem is equivalent (under the assumption of the axiom of choice) to that of fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moser Spindle
In graph theory, a branch of mathematics, the Moser spindle (also called the Mosers' spindle or Moser graph) is an undirected graph, named after mathematicians Leo Moser and his brother William, with seven vertices and eleven edges. It is a unit distance graph requiring four colors in any graph coloring, and its existence can be used to prove that the chromatic number of the plane is at least four.. The Moser spindle has also been called the Hajós graph after György Hajós, as it can be viewed as an instance of the Hajós construction. However, the name "Hajós graph" has also been applied to a different graph, in the form of a triangle inscribed within a hexagon. Construction As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John R
John R. (born John Richbourg, August 20, 1910 - February 15, 1986) was an American radio disc jockey who attained fame in the 1950s and 1960s for playing rhythm and blues music on Nashville radio station WLAC. He was also a notable record producer and artist manager. Richbourg was arguably the most popular and charismatic of the four announcers at WLAC who showcased popular African-American music in nightly programs from the late 1940s to the early 1970s. (The other three were Gene Nobles, Herman Grizzard, and Bill "Hoss" Allen.) Later rock music disc jockeys, such as Alan Freed and Wolfman Jack, mimicked Richbourg's practice of using speech that simulated African-American street language of the mid-twentieth century. Richbourg's highly stylized approach to on-air presentation of both music and advertising earned him popularity, but it also created identity confusion. Because Richbourg and fellow disc jockey Allen used African-American speech patterns, many listeners thought that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noam Elkies
Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At the age of 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist, chess national master and a chess composer. Early life Elkies was born to an engineer father and a piano teacher mother. He attended Stuyvesant High School in New York City for three years before graduating in 1982 at age 15. A child prodigy in 1981, at age 14, he was awarded a gold medal at the 22nd International Mathematical Olympiad, receiving a perfect score of 42, one of the youngest to ever do so. He went on to Columbia University, where he won the Putnam competition at the age of sixteen years and four months, making him one of the youngest Putnam Fellows in history. He was a Putnam Fellow two more times during his undergraduate years. He graduated valedictorian of his class in 1985. He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Ellenberg
Jordan Stuart Ellenberg (born October 30, 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison. His research involves arithmetic geometry. He is also an author of both fiction and non-fiction writing. Early life Ellenberg was born in Potomac, Maryland. He was a child prodigy who taught himself to read at the age of two by watching ''Sesame Street''. His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says ' Bethesda is to the right.'" In second grade, he helped his teenage babysitter with her math homework. By fourth grade, he was participating in high school competitions (such as the American Regions Mathematics League) as a member of the Montgomery County math team. And by eighth grade, he had started college-level work. He was part of the Johns Hopkins University Study of Mathematically Precocious Youth longitudinal cohort. He scored a perfec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAT Solver
The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Scholastic Assessment Test, then the SAT I: Reasoning Test, then the SAT Reasoning Test, then simply the SAT. The SAT is wholly owned, developed, and published by the College Board, a private, not-for-profit organization in the United States. It is administered on behalf of the College Board by the Educational Testing Service, which until recently developed the SAT as well. The test is intended to assess students' readiness for college. The SAT was originally designed not to be aligned with high school curricula, but several adjustments were made for the version of the SAT introduced in 2016, and College Board president David Coleman has said that he also wanted to make the test reflect more closely what students learn in high school with the ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scott Aaronson
Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. His primary areas of research are quantum computing and computational complexity theory. Early life and education Aaronson grew up in the United States, though he spent a year in Asia when his father—a science writer turned public-relations executive—was posted to Hong Kong. He enrolled in a school there that permitted him to skip ahead several years in math, but upon returning to the US, he found his education restrictive, getting bad grades and having run-ins with teachers. He enrolled in The Clarkson School, a gifted education program run by Clarkson University, which enabled Aaronson to apply for colleges while only in his freshman year of high school. He was accepted into Cornell University, where he obtained his BSc in computer science in 2000, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gil Kalai
Gil Kalai (born 1955) is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics and of computer science at Yale University, United States. Biography Kalai received his PhD from Hebrew University in 1983, under the supervision of Micha Perles, and joined the Hebrew University faculty in 1985 after a postdoctoral fellowship at the Massachusetts Institute of Technology.Profile at the Technical University of Eindhoven as an instructor of a minicourse on polyhedral combinatorics. He was the recipient of the Pólya Prize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aubrey De Grey
Aubrey David Nicholas Jasper de Grey (; born 20 April 1963) is an English author and biomedical gerontologist. He is the author of ''The Mitochondrial Free Radical Theory of Aging'' (1999) and co-author of ''Ending Aging'' (2007). He is known for his view that medical technology may enable human beings alive today not to die from age-related causes.Hang in There: The 25-Year Wait for Immortality www.livescience.com. As an amateur mathematician, he has contributed to the study of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solomon W
Solomon (; , ),, ; ar, سُلَيْمَان, ', , ; el, Σολομών, ; la, Salomon also called Jedidiah ( Hebrew: , Modern: , Tiberian: ''Yăḏīḏăyāh'', "beloved of Yah"), was a monarch of ancient Israel and the son and successor of David, according to the Hebrew Bible and the Old Testament. He is described as having been the penultimate ruler of an amalgamated Israel and Judah. The hypothesized dates of Solomon's reign are 970–931 BCE. After his death, his son and successor Rehoboam would adopt harsh policy towards the northern tribes, eventually leading to the splitting of the Israelites between the Kingdom of Israel in the north and the Kingdom of Judah in the south. Following the split, his patrilineal descendants ruled over Judah alone. The Bible says Solomon built the First Temple in Jerusalem, dedicating the temple to Yahweh, or God in Judaism. Solomon is portrayed as wealthy, wise and powerful, and as one of the 48 Jewish prophets. He is also the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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