remaining primitive Pythagoreantriples of numbers up to 300: Euclid's formula is a fundamental formulaforgeneratingPythagoreantriples given an arbitrary...
all primitive Pythagoreantriples are described in Tree of primitive Pythagoreantriples and in FormulasforgeneratingPythagoreantriples. The root node...
zero (thus allowing Pythagoreantriples to be included) with the only condition being that d > 0. In this setting, a Pythagorean quadruple (a, b, c, d)...
of all nodes giving all (and only) primitive Pythagoreantriples without duplication. A Pythagoreantriple is a set of three positive integers a, b, and...
forgenerating special Pythagoreantriples. The rule attributed to Pythagoras (c. 570 – c. 495 BC) starts from an odd number and produces a triple with...
to form Pythagoreantriples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles. Each such triple has the...
primitive Pythagoreantriples (the ones in which the two sides and hypotenuse have no common factor), derive the standard formulaforgenerating all primitive...
examples: Hindin, H. J. (1983). "Stars, hexes, triangular numbers and Pythagoreantriples". J. Rec. Math. 16: 191–193. Deza, Elena; Deza, M. (2012). Figurate...
Solver Competition. Cube-and-Conquer was used to solve the Boolean Pythagoreantriples problem. Cube-and-Conquer is a modification or a generalization of...
three integer sides are known as a Pythagoreantriple or Pythagorean triplet or Pythagorean triad. All Pythagoreantriples ( a , b , c ) {\displaystyle (a...
is the hypotenuse of a Pythagoreantriple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagoreantriples where the two longest sides...
Pythagoreantriples problem required the generation of 200 terabytes of proof. 2017 Marijn Heule, who coauthored solution to the Boolean Pythagorean triples...
his Brāhmasphuṭasiddhānta, Brahmagupta provides a formula useful forgeneratingPythagoreantriples: 12.39. The height of a mountain multiplied by a given...
transforms a Pythagoreantriple into another Pythagoreantriple, only one of the two cases is sufficient for producing all primitive Pythagoreantriples. The...
Archive for History of Exact Sciences, vol 18. (Staal 1999) (Hayashi 2003, p. 118) (Hayashi 2005, p. 363) Pythagoreantriples are triples of integers...
infinitude of Euler bricks can be generated with Saunderson's parametric formula. Let (u, v, w) be a Pythagoreantriple (that is, u2 + v2 = w2.) Then: 105 ...
} Putting k = 2 in this formula, one gets again the formulas of the end of above section Matrix form. The generating function of the Fibonacci sequence...
bisector of A L {\displaystyle AL} . When generating a primitive automedian triangle from a primitive Pythagoreantriple using the Euclidean parameters m , n...
(July 2001), "An alternative characterisation of all primitive Pythagoreantriples", Mathematical Gazette, 85: 273–275, doi:10.2307/3622017. Klaus Pommerening...
"Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagoreantriples, and the Babylonian triangle parameter equations". Historia Mathematica...
MR 1573734 Mitchell, Douglas W. (November 2003), "87.57 Using Pythagoreantriples to generate square roots of I 2 {\displaystyle I_{2}} ", The Mathematical...
680, and 697, forming four right triangle faces described by the Pythagoreantriples (153,104,185), (104,672,680), (153,680,697), and (185,672,697). Eight...
lengths (5, 5, 6) and (5, 5, 8) and area 12. More generally, given two Pythagoreantriples ( a , b , c ) {\displaystyle (a,b,c)} and ( a , d , e ) {\displaystyle...
values. In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence...
Global Information