A Pythagorean quadruple is a tuple of integers a, b, c, and d, such that a2 + b2 + c2 = d2. They are solutions of a Diophantine equation and often only...
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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...
81 KB (11,397 words) - 20:39, 1 September 2024
the hypotenuse Pythagorean triple – a set of three positive integers that can occur in the Pythagorean theorem Pythagorean quadruple - a set of four...
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square of the inverse of the integer altitude from the hypotenuse. Pythagorean quadruples are sets of four integers such that the sum of the squares of the...
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the components of the velocity vector are exactly those from the Pythagorean quadruple parametrization. Other choices of density and pressure are possible...
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equation attributed to Jacobi and Madden Prouhet–Tarry–Escott problem Pythagorean quadruple – Four integers where the sum of the squares of three equals the...
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Jacobi–Madden equation Prouhet–Tarry–Escott problem Beal's conjecture Pythagorean quadruple Generalized taxicab number Sums of powers, a list of related conjectures...
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especially smallest solution for k = 4) Prouhet–Tarry–Escott problem Pythagorean quadruple Sums of powers, a list of related conjectures and theorems L. J...
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Jacobi–Madden equation Prouhet–Tarry–Escott problem Taxicab number Pythagorean quadruple Sums of powers, a list of related conjectures and theorems Distributed...
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Euler brick (category Pythagorean theorem)
323; and body diagonals 374, 300, 278, and 272. Pythagorean quadruple Wacław Sierpiński, Pythagorean Triangles, Dover Publications, 2003 (orig. ed. 1962)...
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Vector algebra relations (redirect from Quadruple product)
\right\|\left\|\mathbf {B} \right\|}}\quad (-\pi <\theta \leq \pi )} The Pythagorean trigonometric identity then provides: ‖ A × B ‖ 2 + ( A ⋅ B ) 2 = ‖ A...
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Flat (music) (redirect from Quadruple flat)
the 100 cents lower used in 12 TET, and the 113.7 cents lower used in Pythagorean tuning. In well temperaments, a flat is two or more different sizes,...
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of a semitone, an interval known as the Pythagorean comma. If limited to twelve pitches per octave, Pythagorean tuning markedly shortens the width of one...
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Beal's conjecture Prouhet–Tarry–Escott problem Taxicab number Pythagorean quadruple Lander, Parkin, and Selfridge conjecture Sums of powers, a list...
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equation Lander, Parkin, and Selfridge conjecture Taxicab number Pythagorean quadruple Sums of powers, a list of related conjectures and theorems Discrete...
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comma ≈ 1⁄344 pythagorean comma). Thus, 53 tone equal temperament is for all practical purposes equivalent to an extended Pythagorean tuning. After Mercator...
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Accidental (music) (redirect from Quadruple accidentals)
the tempered sharp and flat. They presuppose a Pythagorean division of the octave taking the Pythagorean comma (about an eighth of the tempered tone, actually...
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serve beer in mustache cups." Fuddling cup Noggin (cup) Plastic cup Pythagorean cup Frost, Natasha (May 31, 2017). "A Look Back at the Mustache Cups...
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Multiple integral (redirect from Quadruple integral)
^{2}\left(\cos ^{2}\varphi +\sin ^{2}\varphi \right)=\rho ^{2}} using the Pythagorean trigonometric identity (can be useful to simplify this operation). The...
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Amicable numbers (redirect from Amicable quadruple)
unsolved problems in mathematics) Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by...
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Haidao Suanjing which dealt with using Pythagorean theorem (already known by the 9 chapters), and triple, quadruple triangulation for surveying; his accomplishment...
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Sloane, N. J. A. (ed.). "Sequence A088959 (Lowest numbers which are d-Pythagorean decomposable, i.e., square is expressible as sum of two positive squares...
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just fifth is the basis of Pythagorean tuning; the difference between twelve just fifths and seven octaves is the Pythagorean comma. The sum of all n-choose...
39 KB (3,855 words) - 18:32, 6 September 2024
mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing...
22 KB (3,246 words) - 11:08, 23 February 2024
Hanoi at cut-the-knot Real-time GPU generated Sierpinski Triangle in 3D Pythagorean triangles, Waclaw Sierpinski, Courier Corporation, 2003 A067771 Number...
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root quadruple of the largest four largest circles and four smallest curvatures. This quadruple can be found, starting from any other quadruple from the...
50 KB (6,368 words) - 21:18, 29 July 2024
of things are those which can be mathematized and denies that he is a Pythagorean, insisting that numbers do not exhaust the world but simply point to...
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{\displaystyle x} -axis of a semicircle (the square root is a consequence of the Pythagorean theorem), and the integral computes the area below the semicircle. The...
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made such rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud, said...
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between one musical note and another with one-quarter the wavelength or quadruple the frequency. It has also been referred to as the bisdiapason. The fourth...
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