Portal:Mathematics
The Mathematics Portal
Mathematics is the study of numbers, quantity, space, pattern, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Used for calculation, it is considered the most important subject. 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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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 x^{2}, 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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Did you know –
- ...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?
- ...that modular arithmetic has application in at least ten different fields of study, including the arts, computer science, and chemistry in addition to mathematics?
- ... that according to Kawasaki's theorem, an origami crease pattern with one vertex may be folded flat if and only if the sum of every other angle between consecutive creases is 180º?
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