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...
82 KB (11,398 words) - 23:28, 20 June 2025
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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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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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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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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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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Jacobi–Madden equation Prouhet–Tarry–Escott problem Beal conjecture Pythagorean quadruple Generalized taxicab number Sums of powers, a list of related conjectures...
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Euler brick (category Pythagorean theorem)
congruent number elliptic curve of rank at least 2. 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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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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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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Flat (music) (redirect from Quadruple flat)
intonation a flat commonly lowers a note's pitch by 70.57 cents. In Pythagorean tuning a flat lowers the pitch by 113.7 cents, and in well temperaments...
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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 numbers can be extended to finding perfect cubes,Pythagorean triples and Pythagorean quadruples, and then goes on to provide a classification of different...
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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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Taki, favors a Moustache cup. Fuddling cup Noggin (cup) Plastic cup Pythagorean cup Frost, Natasha (May 31, 2017). "A Look Back at the Mustache Cups...
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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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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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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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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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root quadruple of the largest four largest circles and four smallest curvatures. This quadruple can be found, starting from any other quadruple from the...
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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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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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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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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...
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powers of 4 (45 + 40); Jacobsthal-Lucas number; hypotenuse of primitive Pythagorean triangle 1026 = sum of two distinct powers of 2 (1024 + 2) 1027 = sum...
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Lee and Alistair B. Fraser, "Despite its many flaws and its appeal to Pythagorean numerology, Aristotle's qualitative explanation showed an inventiveness...
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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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