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Euclidean Tilings
Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of Euclid, an ancient Greek mathematician. It is the name of: Geometry *Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations *Euclidean geometry, the study of the properties of Euclidean spaces *Non-Euclidean geometry, systems of points, lines, and planes analogous to Euclidean geometry but without uniquely determined parallel lines *Euclidean distance, the distance between pairs of points in Euclidean spaces * Euclidean ball, the set of points within some fixed distance from a center point Number theory *Euclidean division, the division which produces a quotient and a remainder *Euclidean algorithm, a method for finding greatest common divisors *Extended Euclidean algorithm, a method for solving the Diophantine equation ''ax'' + ''by'' = ''d'' where ''d'' is the greatest common divisor of ''a'' and ''b'' *Eu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken for the earlier philosopher Euclid of Megara, causing his biograph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of integers. This generalized Euclidean algorithm can be put to many of the same uses as Euclid's original algorithm in the ring of integers: in any Euclidean domain, one can apply the Euclidean algorithm to compute the greatest common divisor of any two elements. In particular, the greatest common divisor of any two elements exists and can be written as a linear combination of them (Bézout's identity). Also every ideal in a Euclidean domain is principal, which implies a suitable generalization of the fundamental theorem of arithmetic: every Euclidean domain is a unique factorization domain. It is important to compare the class of Euclidean domains with the larger class of principal ideal domains (PIDs). An arbitrary PID has much the same "s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions ( theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's ''Elements'' has been referred to as the most successful and influential textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid (other)
Euclid, Euclides, or Eucleides generally refers to the ancient Greek mathematician Euclid of Alexandria (3rd century BC), who wrote a work on geometry called the ''Elements''. It may also refer to: People * Euclid of Megara (c. 435 BC–c. 365 BC), ancient Greek philosopher * Eucleides, archon of Athens (5th century BC) * Euclid Bertrand (born 1974), Dominican former footballer * Euclides da Cunha (1866–1909), Brazilian sociologist * Euclid Kyurdzidis (born 1968), Russian actor * Euclid Tsakalotos (born 1960), Greek economist and Minister of Finance * Nicholas Euclid (1932–2007), Australian rugby league player, coach, and official Mathematics, science, and technology * Euclid Contest, a maths competition held by the Centre for Education in Mathematics and Computing * Euclid (programming language) * Euclid (computer program) * Euclid, a computer system used by Euroclear * Euclid (spacecraft), a space telescope built by ESA, to be launched in Feb 2023 * Euclidean space * 4354 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intermediate Math League Of Eastern Massachusetts
The Intermediate Math League of Eastern Massachusetts (or IMLEM) is a math league for middle schools across Eastern Massachusetts. A brief history of IMLEM is given in its By-Laws: Schools As of 2017, 86 different schools attend the competition. Each school is allowed to send more than 1 team and each team can consist of at most 10 people. Alternates, people who are not officially part of team, can be taken too. There are a total of 15 different geographic clusters of schools and there is even a cluster of schools from Pennsylvania. The schools are then separated into different divisions with the schools in each division be approximately the same level. Schools can then make their way up through divisions to try to get into the top division, which is the Lexington Division. In total there are 13 divisions. Schools may send more than one team, however no student can compete on more than one team in a year. Also, a school may send alternates to gain the experience of a meet. Meet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
