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 the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
- ... that Catechumen, a Christian first-person shooter, was funded only in the aftermath of the Columbine High School massacre?
- ... that after Florida schools banned 54 mathematics books, Chaz Stevens petitioned that they also ban the Bible?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... that people in Madagascar perform algebra on tree seeds in order to tell the future?
- ... that Green Day's "Wake Me Up When September Ends" became closely associated with the aftermath of Hurricane Katrina?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
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- … 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?
- … that the best known lower bound for the length of the smallest superpermutation was first posted anonymously to the internet imageboard 4chan?
- ...that the mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
- ...that a regular heptagon is the regular polygon with the fewest sides which is not constructible with a compass and straightedge?
- ...that the regular trigonometric functions and the hyperbolic trigonometric functions can be related without using complex numbers through the Gudermannian function?
- ...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?
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The graph of a real-valued quadratic function of a real variable x, is a parabola. Image credit: Enoch Lau |
A quadratic equation is a polynomial equation of degree two. The general form is
where a ≠ 0 (if a = 0, then the equation becomes a linear equation). The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x2, the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term.
Quadratic equations are known by that name because quadratus is Latin for "square"; in the leading term the variable is squared.
A quadratic equation has two (not necessarily distinct) solutions, which may be real or complex, given by the quadratic formula:
If the discriminant , then the quadratic equation has two distinct real solutions; if , the equation has two real solutions which are equal; if , the equation has two complex solutions.
These solutions are roots of the corresponding quadratic function
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