Portal:Mathematics
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... that mathematics professor Ari Nagel has fathered more than a hundred children?
- ... that owner Matthew Benham influenced both Brentford FC in the UK and FC Midtjylland in Denmark to use mathematical modelling to recruit undervalued football players?
- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that despite a mathematical model deeming the ice cream bar flavour Goody Goody Gum Drops impossible, it was still created?
- ...that i to the power of i, where i is the square root of -1, is a real number?
- ...an infinite, nonrepeating decimal can be represented using only the number 1 using continued fractions?
- ...that 253931039382791 and the following 18 prime numbers all end in the digit 1?
- ...that the Electronic Frontier Foundation funds awards for the discovery of prime numbers beyond certain sizes?
- ...that pi can be computed using only the number 2 by the work of Viète?
- … that the Riemann Hypothesis, one of the Millennium Problems, depends on the asymptotic growth of the Mertens Function?
- … that every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater?
Example of a Persian design with wallpaper group type "p6m" Image credit: Owen Jones |
A wallpaper group is a mathematical concept used to classify repetitive designs on two-dimensional surfaces, such as floors and walls, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The mathematical study of such patterns reveals that exactly 17 different types of pattern can occur.
Wallpaper groups are examples of an abstract algebraic structure known as a group. Groups are frequently used in mathematics to study the notion of symmetry. Wallpaper groups are related to the simpler frieze groups, and to the more complex three-dimensional crystallographic groups. (Full article...)
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