In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements . It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations.
In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers, or defined as generalizations of the integers.
Peter Williston Shor is an American professor of applied mathematics at MIT. He is known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer.
David Harold Bailey is a mathematician and computer scientist. He received his B.S. in mathematics from Brigham Young University in 1972 and his Ph.D. in mathematics from Stanford University in 1976. He worked for 14 years as a computer scientist at NASA Ames Research Center, and then from 1998 to 2013 as a Senior Scientist at the Lawrence Berkeley National Laboratory. He is now retired from the Berkeley Lab.
Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.
Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit."
Clifford Alan Pickover is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was employed at the IBM Thomas J. Watson Research Center in Yorktown, New York, where he was editor-in-chief of the IBM Journal of Research and Development. He has been granted more than 700 U.S. patents, is an elected Fellow for the Committee for Skeptical Inquiry, and is author of more than 50 books, translated into more than a dozen languages.
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, could be computed using a skein relation, although its significance was not realized until the discovery of the Jones polynomial in 1984. Soon after Conway's reworking of the Alexander polynomial, it was realized that a similar skein relation was exhibited in Alexander's paper on his polynomial.
Peter Benjamin Borwein was a Canadian mathematician and a professor at Simon Fraser University. He is known as a co-author of the paper which presented the Bailey–Borwein–Plouffe algorithm for computing π.
The umbilic torus or umbilic bracelet is a single-edged 3-dimensional shape. The lone edge goes three times around the ring before returning to the starting point. The shape also has a single external face. A cross section of the surface forms a deltoid.
Jean-Pierre Hébert was an American artist of French origin. He specialized in algorithmic art, drawings, and mixed media. He co-founded the Algorists in 1995 with Roman Verostko. From 2003 until his death, he held an artist-in-residence position at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara.
Akshay Venkatesh is an Australian mathematician and a professor at the School of Mathematics at the Institute for Advanced Study. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces, ergodic theory, and algebraic topology.
An integer relation between a set of real numbers x1, x2, ..., xn and a set of integers a1, a2, ..., an, not all 0, such that
Nuclear Energy (1964–1966) is a bronze sculpture by Henry Moore on the campus of the University of Chicago at the site of the world's first nuclear reactor, Chicago Pile-1. The first human-made self-sustaining nuclear chain reaction was created here on December 2, 1942. The sculpture is set in a granite paved quadrangle, with the paving stones radiating outward from the sculpture, and memorial plaques mounted on a adjacent wall. The memorial site is a National Historic Landmark and Chicago Landmark.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
The Bailey–Borwein–Plouffe formula is a formula for π. It was discovered in 1995 by Simon Plouffe and is named after the authors of the article in which it was published, David H. Bailey, Peter Borwein, and Plouffe. Before that, it had been published by Plouffe on his own site. The formula is:
A statue of Abraham Lincoln by American artist Gaetano Cecere is installed along Lincoln Memorial Drive in Milwaukee, Wisconsin, United States. The 10'6" bronze sculpture depicts a young beardless Abraham Lincoln. The former president stands looking down with both hands at his sides.
Rhythm of Structure is a multimedia interdisciplinary project founded in 2003. It features a series of exhibitions, performances, and academic projects that explore the interconnecting structures and process of mathematics and art, and language, as way to advance a movement of mathematical expression across the arts, across creative collaborative communities celebrating the rhythm and patterns of both ideas of the mind and the physical reality of nature.
