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- ...third is tangent to the first circle and the <math>y</math>-axis. A circle of radius <math>r > s</math> is tangent to both axes and to the second and thi ...the [[x-axis]], and draw the perpendicular from this radius to the center of the third circle. This gives us a [[right triangle]] with legs <math>r-3,r-2 KB (307 words) - 23:58, 17 November 2024
- ...rs of Mathematics], and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up ...etry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MATHCOUNTS curriculum is in developing [[mathematical problem solving]] ski10 KB (1,504 words) - 13:10, 1 December 2024
- ...' are recommended by [[Art of Problem Solving]] administrators and members of the [http://aops.com/community AoPS Community]. Levels of reading and math ability are loosely defined as follows:24 KB (3,202 words) - 14:33, 13 January 2025
- ...raft. Mathematics provides a kind of "quality control" for the development of trustworthy theories and equations which are important to people in most mo ...matics which are given to be true. Mathematicians then use various methods of formal [[proof]] to extend the axioms to come up with surprising and elegan6 KB (866 words) - 06:57, 17 January 2025
- ...on]] methods. While most of the subject of inequalities is often left out of the ordinary educational track, they are common in [[mathematics Olympiads] ...]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four signs: <math>>,<,\ge,\le</math>.12 KB (1,806 words) - 05:07, 19 June 2024
- ...on certain math topics not commonly taught in school, as well as practices of previous years' team rounds. Please email Xinke Guo-Xue at xinkeguoxue@gmai ...s organized by and practices at the San Diego Math Circle (SDMC), and most of the students on last year's team were regular attendees at SDMC. Also, sinc22 KB (3,532 words) - 10:25, 27 September 2024
- ...he four individual tests (algebra, combinatorics, geometry, number theory) of their choice. Each individual test is 60 minutes long. Books, calculators In the Team Test, members of a team work together to solve problems, usually within 30 minutes.2 KB (295 words) - 22:19, 5 January 2019
- ...oice test with 4 choices and an extra choice called NOTA, which means None Of The Above. Test topics usually follow school curriculum subjects; however t You may only take one type of test a year for every competition, depending on how many competitions your4 KB (632 words) - 17:21, 21 December 2024
- ...verse are provided: an elementary one that rests close to basic principles of [[modular arithmetic]], and an elegant method that relies on more powerful ...;a contradiction.) This inverse is unique, and each number is the inverse of its inverse. If one integer <math>a</math> is its own inverse, then4 KB (639 words) - 00:53, 2 February 2023
- ...'''trivial inequality''' is an [[inequality]] that states that the square of any real number is nonnegative. Its name comes from its simplicity and stra ...th>, then <math>x^2 = (-x)(-x) > 0,</math> again by the closure of the set of positive numbers under multiplication.3 KB (583 words) - 20:20, 2 August 2024
- ...all the numbers, divided by the number of numbers - the [[average]] of the set. If we let <math>{AM}</math> denote Arithmetic Mean, is the arithmetic mean of the <math>{n}</math> numbers <math>x_1,x_2,\ldots,x_n</math>.699 bytes (110 words) - 11:44, 20 September 2015
- ...ltiplied by [[coefficient]]s from a predetermined [[set]] (usually the set of integers; [[rational]], [[real]] or [[complex]] numbers; but in [[abstract ...h coefficient and <math>a_n \neq 0</math>. Often, the leading coefficient of a polynomial will be equal to 1. In this case, we say we have a ''monic''6 KB (1,100 words) - 14:57, 30 August 2024
- ...may be referred to as the '''Dirichlet box principle'''. A common phrasing of the principle uses balls and boxes and is that if <math>n</math> balls are An intuitive proof of the pigeonhole principle is as follows: suppose for contradiction that ther11 KB (1,986 words) - 18:13, 19 June 2024
- ...ains similar at every scale. This concept of self-similarity is a hallmark of fractals, making them distinct from more traditional geometric shapes. ...even clouds display fractal-like properties. The roughness and complexity of these natural formations can be described and understood through fractal ge2 KB (302 words) - 10:17, 27 September 2024
- '''Trigonometric substitution''' is the technique of replacing [[variable]]s in equations with <math>\sin \theta\,</math> or <ma In [[calculus]], it is used to evaluate [[integral]]s of [[expression]]s such as <math>\sqrt{a^2+x^2},\sqrt{a^2-x^2}</math> or <math1 KB (173 words) - 17:42, 30 May 2021
- ...[[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets. Here, we will illustrate how PIE is applied with various numbers of sets.9 KB (1,703 words) - 00:20, 7 December 2024
- ...ing the number of combinations of size <math>r</math> from an original set of size <math>n</math> ...denoting the number of combinations of <math>{r}</math> objects from a set of <math>{n}</math> objects is:4 KB (638 words) - 20:55, 5 January 2025
- ...nction in [[combinatorics]] and [[analysis]], used to determine the number of ways to arrange objects. By [[mathematical convention|convention]] and rules of an empty product, <math>0!</math> is given the value <math>1</math>.10 KB (809 words) - 15:40, 17 March 2024
- ...more at the introductory level if they have a hard time following the rest of this article). This theorem is credited to [[Pierre de Fermat]]. ...a \pmod {p}</math>. As you can see, it is derived by multipling both sides of the theorem by <math>a</math>. The restated form is nice because we no lon16 KB (2,660 words) - 22:42, 28 August 2024
- ...<math>n</math> is a positive integer, <math>\phi{(n)}</math> is the number of integers in the range <math>\{1,2,3\cdots{,n}\}</math> which are relatively This theorem is credited to [[Leonhard Euler]]. It is a generalization of [[Fermat's Little Theorem]], which specifies it when <math>{m}</math> is pr4 KB (569 words) - 21:34, 30 December 2024