Portal:Mathematics
The Mathematics Portal
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...)
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- ... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882?
- ... that Fairleigh Dickinson's upset victory over Purdue was the biggest upset in terms of point spread in NCAA tournament history, with Purdue being a 23+1⁄2-point favorite?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... that despite a mathematical model deeming the ice cream bar flavour Goody Goody Gum Drops impossible, it was still created?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that ten-sided gaming dice have kite-shaped faces?
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- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory?
- ...that the Pythagorean Theorem generalizes to any three similar shapes on the three sides of a right-angled triangle?
- ...that the orthocenter, circumcenter, centroid and the centre of the nine-point circle all lie on one line, the Euler line?
- ...that an arbitrary quadrilateral will tessellate?
- ...that it has not been proven whether or not every even integer greater than two can be expressed as the sum of two primes?
- ...that the sum of the first n odd numbers divided by the sum of the next n odd numbers is always equal to one third?
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A number is an abstract object that represents a count or measurement. A symbol for a number is called a numeral. The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.
Numbers can be classified into sets called number systems. The most familiar numbers are the natural numbers, which to some mean the non-negative integers and to others mean the positive integers. In everyday parlance the non-negative integers are commonly referred to as whole numbers, the positive integers as counting numbers, symbolised by . Mathematics is used in many classes throughout the course of one's education.
The integers consist of the natural numbers (positive whole numbers and zero) combined with the negative whole numbers, which are symbolised by (from the German Zahl, meaning "number").
A rational number is a number that can be expressed as a fraction with an integer numerator and a non-zero natural number denominator. Fractions can be positive, negative, or zero. The set of all fractions includes the integers, since every integer can be written as a fraction with denominator 1. The symbol for the rational numbers is a bold face (for quotient). (Full article...)
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