# 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

And that is true

## Triangles

 And when you make a triangle with sides a, b and c it will be a right angled triangle (see Pythagoras' Theorem for more details): Note: c is the longest side of the triangle, called the "hypotenuse" a and b are the other two sides

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

Here are some more examples:

 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) (11,60,61) (12,35,37) (13,84,85) (15,112,113) (16,63,65) (17,144,145) (19,180,181) (20,21,29) (20,99,101) (21,220,221) (23,264,265) (24,143,145) (25,312,313) (27,364,365) (28,45,53) (28,195,197) (29,420,421) (31,480,481) (32,255,257) (33,56,65) (33,544,545) (35,612,613) (36,77,85) (36,323,325) (37,684,685) ... infinitely many more ...

## Scale Them Up

The simplest way to create further Pythagorean Triples is to scale up a set of triples.

### Example: scale 3,4,5 by 2 gives 6,8,10

Which also fits the formula a2 + b2 = c2:

62 + 82 = 102

36 + 64 = 100