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# Pythagorean Triples

Pythagoras was a 6th century BC philosopher and mathematician who is famous for articulating the classic right triangle relationship a2+b2=c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Sets of (a, b, c) where all three lengths are integers are called Pythagorean Triples. In the study of the Pythagorean Theorem, students become familiar with the smaller Pythagorean Triples, such as (3, 4, 5) and (5, 12, 13).

The JavaScript applet below generates Pythagorean Triples of increasing value. It can be used to locate Pythagorean Triples of significant size. You can select whether you want all results shown, or just the non-trivial ones. Trivial Pythagorean Triples are multiples of other triples. For example, (6, 8, 10) is a trivial triple because it's a multiple of the smaller triple (3, 4, 5). The math checks on this:

62 + 82 = 102

(2*3)2 + (2*4)2 = (2*5)2

22 * 32 + 22 * 42 = 22 * 52

22(32 + 42) = 22(52)

32 + 42 = 52

## Pythagorean Triple Calculator

Ouput options

### Credits

• Original Java Applet by Nick Exner (1998)
• Modified by Michael McKelvey (2001)
• JavaScript+HTML5 Remake by Evan Ramos (2014)

### Calculator Programs for the TI-83 and TI-89, Get Graph-Link to View

Calculator programs written by James P. Dildine, 1999.