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Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If ( a , b , c ) is a Pythagorean triple, then so is ( ka , kb , kc ) for any positive integer k . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle .
Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same.
The quadratic formula, which concisely expresses the solutions of all quadratic equations The Rubik's Cube group is a concrete application of group theory. [26] Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra.
A well-studied example is the cyclic quadrilateral. Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called a bicentric polygon. A hypocycloid is a curve that is inscribed in a given circle by tracing a fixed point on a smaller circle that rolls within and tangent to the given circle.
A probability sample is a sample in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their ...
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