Tool to generate Pythagorean triples. A Pythagorean triple is a set of three natural numbers a, b, and c, such that a^2+b^2=c^2, for example (3,4,5) is a Triple of Pythagore: 3^2+4^2=5^2

Pythagore Triple - dCode

Tag(s) : Mathematics, Geometry

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Tool to generate Pythagorean triples. A Pythagorean triple is a set of three natural numbers a, b, and c, such that a^2+b^2=c^2, for example (3,4,5) is a Triple of Pythagore: 3^2+4^2=5^2

It exists heuristics but the simple method consists in testing iteratively all possibilities of a and b when s is given, the value of c is constrained by s=a+b+c.

The following equations can be deducted:

$$ a^2 + b^2 = (s − a − b)^2 \\ a <= (s − 3)/3 \\ b < (s − a)/2 $$

Example: Consider \( s = 12 \), then \( a <= 3 \) and \( b < 4.5 \), a quick test allows to find \( a = 3, b = 4 \) and get the triple \( \{3,4,5\} \).

The first Pythagorean triples (side inferior to 100)

3,4,5 | 5,12,13 | 6,8,10 |

7,24,25 | 8,15,17 | 9,12,15 |

9,40,41 | 10,24,26 | 11,60,61 |

12,16,20 | 12,35,37 | 13,84,85 |

14,48,50 | 15,20,25 | 15,36,39 |

16,30,34 | 16,63,65 | 18,24,30 |

18,80,82 | 20,21,29 | 20,48,52 |

21,28,35 | 21,72,75 | 24,32,40 |

24,45,51 | 24,70,74 | 25,60,65 |

27,36,45 | 28,45,53 | 28,96,100 |

30,40,50 | 30,72,78 | 32,60,68 |

33,44,55 | 33,56,65 | 35,84,91 |

36,48,60 | 36,77,85 | 39,52,65 |

39,80,89 | 40,42,58 | 40,75,85 |

42,56,70 | 45,60,75 | 48,55,73 |

48,64,80 | 51,68,85 | 54,72,90 |

57,76,95 | 60,63,87 | 60,80,100 |

65,72,97 |

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