How to Find Pythagorean Triples

Pythagorean triples are often used in geometry. A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem: a2 + b2 = c2 ("a" squared plus "b" squared equals "c" squared). These triples exist within some right triangles, with "a" and "b" being legs of the triangle and "c" being the hypotenuse. One of the simplest methods of finding many Pythagorean triples requires only basic math skills.

Things You'll Need

• calculator (optional)

Instructions

1. Consider the basic Pythagorean triple, which consists of the lowest set of numbers: 3, 4 and 5.

2. Multiply a common factor times each of these lowest numbers. For instance, multiply 3, 4, and 5 by the number 2 to get 6, 8 and 10.

3. Check the new numbers to see if the results satisfy the formula "a2 + b2 = c2." Begin by squaring the first integer:
   6 x 6 = 36

4. Square the second integer:
   8 x 8 = 64

5. Square the third integer:
   10 x 10 = 100

6. Check to see if the products from steps 3 and 4 equal the product in step 5:
   36 + 64 = 100
   Therefore, you can be sure that 6, 8 and 10 are Pythagorean triples.

Tips & Warnings

• Try this process with any number times 3, 4, and 5.

References

• Brown University mathematics website