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...

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...

equation attributed to Jacobi and Madden Prouhet–Tarry–Escott problem Pythagorean quadruple – Four integers where the sum of the squares of three equals the...

Jacobi–Madden equation Prouhet–Tarry–Escott problem Taxicab number Pythagorean quadruple Sums of powers, a list of related conjectures and theorems Distributed...

the components of the velocity vector are exactly those from the Pythagorean quadruple parametrization. Other choices of density and pressure are possible...

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...

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...

Jacobi–Madden equation Prouhet–Tarry–Escott problem Beal conjecture Pythagorean quadruple Generalized taxicab number Sums of powers, a list of related conjectures...

congruent number elliptic curve of rank at least 2. Pythagorean quadruple Wacław Sierpiński, Pythagorean Triangles, Dover Publications, 2003 (orig. ed. 1962)...

\right\|\left\|\mathbf {B} \right\|}}\quad (-\pi <\theta \leq \pi )} The Pythagorean trigonometric identity then provides: ‖ A × B ‖ 2 + ( A ⋅ B ) 2 = ‖ A...

especially smallest solution for k = 4) Prouhet–Tarry–Escott problem Pythagorean quadruple Sums of powers, a list of related conjectures and theorems L. J...

Beal's conjecture Prouhet–Tarry–Escott problem Taxicab number Pythagorean quadruple Lander, Parkin, and Selfridge conjecture Sums of powers, a list...

equation Lander, Parkin, and Selfridge conjecture Taxicab number Pythagorean quadruple Sums of powers, a list of related conjectures and theorems Discrete...

the hypotenuse Pythagorean triple – a set of three positive integers that can occur in the Pythagorean theorem Pythagorean quadruple - a set of four...

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...

square numbers can be extended to finding perfect cubes,Pythagorean triples and Pythagorean quadruples, and then goes on to provide a classification of different...

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...

comma ≈ ⁠1/ 344 ⁠ pythagorean comma). Thus, 53 tone equal temperament is for all practical purposes equivalent to an extended Pythagorean tuning. After Mercator...

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...

unsolved problems in mathematics Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by...

root quadruple of the largest four largest circles and four smallest curvatures. This quadruple can be found, starting from any other quadruple from the...

^{2}\left(\cos ^{2}\varphi +\sin ^{2}\varphi \right)=\rho ^{2}} using the Pythagorean trigonometric identity (can be useful to simplify this operation). The...

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...

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...

Hanoi at cut-the-knot Real-time GPU generated Sierpinski Triangle in 3D Pythagorean triangles, Waclaw Sierpinski, Courier Corporation, 2003 A067771    Number...

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...

made such rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud, said...

Haidao Suanjing which dealt with using Pythagorean theorem (already known by the 9 chapters), and triple, quadruple triangulation for surveying; his accomplishment...

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...

Lee and Alistair B. Fraser, "Despite its many flaws and its appeal to Pythagorean numerology, Aristotle's qualitative explanation showed an inventiveness...