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  • Pythagoras equations
  • How to prove pythagorean theorem

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    Pythagorean Triples

    A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:

    a2 + b2 = c2

    Example: The smallest Pythagorean Triple is 3, 4 and 5.

    Let's check it:

    32 + 42 = 52

    Calculating this becomes:

    9 + 16 = 25

    Yes, it is a Pythagorean Triple!

    Triangles

    When a triangle's sides are a Pythagorean Triple it is a right angled triangle.

    See Pythagoras' Theorem for more details.

    Example: The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle:

     

    Here are two more Pythagorean Triples:

    5, 12, 13 9, 40, 41
       
     
    52 + 122 = 132 92 + 402 = 412
    25 + 144 = 169 (try it yourself)

    And each triangle has a right angle!

    List of the First Few

    Here is a list of the first few Pythagorean Triples (not including "scaled up" versions mentioned below):

    (3, 4, 5)(5, 12, 13)(7, 24, 25)(8, 15, 17)
    (9, 40, 41)(11, 60, 6