Euclid's formula, many other formulas for generating Pythagorean triples have been developed. Euclid's, Pythagoras' and Plato's formulas for calculating...

remaining primitive Pythagorean triples of numbers up to 300: Euclid's formula is a fundamental formula for generating Pythagorean triples given an arbitrary...

55, 73), (65, 72, 97) There are many formulas for generating Pythagorean triples. Of these, Euclid's formula is the most well-known: given arbitrary...

sides produces the same relationship. Using Euclid's formula for generating Pythagorean triples, the sides must be in the ratio m2 − n2 : 2mn : m2 + n2...

method allows retrieving Euclid's formula for generating Pythagorean triples. For retrieving exactly Euclid's formula, we start from the solution (−1,...

all primitive Pythagorean triples are described in Tree of primitive Pythagorean triples and in Formulas for generating Pythagorean triples. The root node...

et Cosmographie (1711) La Perspective (1711). VIII. Formulas for Generating Pythagorean Triples Bernard Le Bovier de Fontenelle (1790) Eloge de Ozanam...

application of the above formula for the square of a binomial is the "(m, n)-formula" for generating Pythagorean triples: For m < n, let a = n2 − m2, b...

primitive Pythagorean triples is a mathematical tree in which each node represents a primitive Pythagorean triple and each primitive Pythagorean triple is represented...

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)...

Earth's geodesy and to navigate the oceans since antiquity. Pythagorean triples are triples of integers ( a , b , c ) {\displaystyle (a,b,c)} with the...

} 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...

primitive Pythagorean triples (the ones in which the two sides and hypotenuse have no common factor), derive the standard formula for generating all primitive...

examples: Hindin, H. J. (1983). "Stars, hexes, triangular numbers and Pythagorean triples". J. Rec. Math. 16: 191–193. Deza, Elena; Deza, M. (2012). Figurate...

to form Pythagorean triples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles. Each such triple has the...

and was later reduced to 850 megabytes. 2016 – Solving the Boolean Pythagorean triples problem required the generation of 200 terabytes of proof. 2017 –...

t} . The curves of this form can be generated by a formula analogous to a formula for generating Pythagorean triples. Let u ( t ) {\displaystyle u(t)} ...

transforms a Pythagorean triple into another Pythagorean triple, only one of the two cases is sufficient for producing all primitive Pythagorean triples up to...

his Brāhmasphuṭasiddhānta, Brahmagupta provides a formula useful for generating Pythagorean triples: 12.39. The height of a mountain multiplied by a given...

three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. All Pythagorean triples ( a , b , c ) {\displaystyle (a...

is the hypotenuse of a Pythagorean triple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagorean triples where the two longest sides...

Solver Competition. Cube-and-Conquer was used to solve the Boolean Pythagorean triples problem. Cube-and-Conquer is a modification or a generalization of...

dated c. 1800 BC. It is a broken clay tablet that contains a list of Pythagorean triples, that is, integers ( a , b , c ) {\displaystyle (a,b,c)} such that...

680, and 697, forming four right triangle faces described by the Pythagorean triples (153,104,185), (104,672,680), (153,680,697), and (185,672,697). Eight...

four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317) and a Harshad number. Nearly all of the palindromic...

Archive for History of Exact Sciences, vol 18. (Staal 1999) (Hayashi 2003, p. 118) (Hayashi 2005, p. 363) Pythagorean triples are triples of integers...

infinitude of Euler bricks can be generated with Saunderson's parametric formula. Let (u, v, w) be a Pythagorean triple (that is, u2 + v2 = w2.) Then: 105 ...

(July 2001), "An alternative characterisation of all primitive Pythagorean triples", Mathematical Gazette, 85: 273–275, doi:10.2307/3622017. Klaus Pommerening...

values. In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence...

lengths (5, 5, 6) and (5, 5, 8) and area 12. More generally, given two Pythagorean triples ( a , b , c ) {\displaystyle (a,b,c)} and ( a , d , e ) {\displaystyle...