Four integers where the sum of the squares of three equals the square of the fourth
All four primitive Pythagorean quadruples with only single-digit values
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 positive integer values are considered.[1] However, to provide a more complete geometric interpretation, the integer values can be allowed to be negative and zero (thus allowing Pythagorean triples to be included) with the only condition being that d > 0. In this setting, a Pythagorean quadruple (a, b, c, d) defines a cuboid with integer side lengths |a|, |b|, and |c|, whose space diagonal has integer length d; with this interpretation, Pythagorean quadruples are thus also called Pythagorean boxes.[2] In this article we will assume, unless otherwise stated, that the values of a Pythagorean quadruple are all positive integers.
A Pythagoreanquadruple 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...
square of the inverse of the integer altitude from the hypotenuse. Pythagoreanquadruples are sets of four integers such that the sum of the squares of the...
equation attributed to Jacobi and Madden Prouhet–Tarry–Escott problem Pythagoreanquadruple – Four integers where the sum of the squares of three equals the...
Jacobi–Madden equation Prouhet–Tarry–Escott problem Taxicab number Pythagoreanquadruple Sums of powers, a list of related conjectures and theorems Distributed...
\right\|\left\|\mathbf {B} \right\|}}\quad (-\pi <\theta \leq \pi )} The Pythagorean trigonometric identity then provides: ‖ A × B ‖ 2 + ( A ⋅ B ) 2 = ‖ A...
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...
comma ≈ 1⁄344 pythagorean comma). Thus, 53 tone equal temperament is for all practical purposes equivalent to an extended Pythagorean tuning. After Mercator...
^{2}\left(\cos ^{2}\varphi +\sin ^{2}\varphi \right)=\rho ^{2}} using the Pythagorean trigonometric identity (can be useful to simplify this operation). The...
unsolved problems in mathematics) Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by...
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...
Haidao Suanjing which dealt with using Pythagorean theorem (already known by the 9 chapters), and triple, quadruple triangulation for surveying; his accomplishment...
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...
mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing...
made such rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud, said...
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...
{\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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