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Pythagorean Triple
A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean triple is one in which , and are coprime (that is, they have no common divisor larger than 1). For example, is a primitive Pythagorean triple whereas is not. Every Pythagorean triple can be scaled to a unique primitive Pythagorean triple by dividing by their greatest common divisor. Conversely, every Pythagorean triple can be obtained by multiplying the elements of a primitive Pythagorean triple by a positive integer (the same for the three elements). The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a^2+b^2=c^2; thus, Pythagorean triples describe the three integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pythagorean Theorem - Ani
Pythagorean, meaning of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras, may refer to: Philosophy * Pythagoreanism, the esoteric and metaphysical beliefs purported to have been held by Pythagoras * Neopythagoreanism, a school of philosophy reviving Pythagorean doctrines that became prominent in the 1st and 2nd centuries AD * Pythagorean diet, the name for vegetarianism before the nineteenth century Mathematics * Pythagorean theorem * Pythagorean triple * Pythagorean prime * Pythagorean trigonometric identity * Table of Pythagoras, another name for the multiplication table Music * Pythagorean comma * Pythagorean hammers * Pythagorean tuning Other uses * Pythagorean cup * Pythagorean expectation, a baseball statistical term * Pythagorean letter See also * List of things named after Pythagoras {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
