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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
Pythagorean trigonometric identity. The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is.
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths [2] which are "pure" or perfect, with ratio :. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio 2 : 1 {\displaystyle 2:1} ), and hence is the ...
Garfield in 1881. Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem invented by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the New-England Journal of Education (Vol. 3, No.14, April 1, 1876). [1][2] At the time of ...
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. 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 ...
Bride's Chair. In geometry, a Bride's Chair is an illustration of the Pythagorean theorem. [1] The figure appears in Proposition 47 of Book I of Euclid's Elements. [2] It is also known by several other names, such as the Franciscan's cowl, peacock's tail, windmill, Pythagorean pants, Figure of the Bride, theorem of the married women, and chase ...
Pythagoras. Pythagoras of Samos[a] (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) [b] was an ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in ...
In 1988, The Theorem of Pythagoras was the first video produced by the series and reviews the Pythagorean theorem. [4] For all right triangles, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a 2 + b 2 = c 2). The theorem is named after Pythagoras of ancient Greece.
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