Portal:Mathematics
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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 multiple mathematics competitions have made use of Sophie Germain's identity?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that Fathimath Dheema Ali is the first Olympic qualifier from the Maldives?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that Olympic historians were unconvinced by speculation that an unknown boy coxswain grew up to be a renowned Georgian mathematician?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that Hannah Fry used mathematics to compare Elizabeth II's Christmas messages with the lyrics of Snoop Dogg?
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- ...that as of April 2010 only 35 even numbers have been found that are not the sum of two primes which are each in a Twin Primes pair? ref
- ...the Piphilology record (memorizing digits of Pi) is 70000 as of Mar 2015?
- ...that people are significantly slower to identify the parity of zero than other whole numbers, regardless of age, language spoken, or whether the symbol or word for zero is used?
- ...that Auction theory was successfully used in 1994 to sell FCC airwave spectrum, in a financial application of game theory?
- ...properties of Pascal's triangle have application in many fields of mathematics including combinatorics, algebra, calculus and geometry?
- ...work in artificial intelligence makes use of swarm intelligence, which has foundations in the behavioral examples found in nature of ants, birds, bees, and fish among others?
- ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?
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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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