University of Illinois at Urbana-Champaign
MSTE
Office for Mathematics, Science, and Technology Education
College of Education @ University of Illinois

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

Calculated Triples

Credits

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

Calculator Programs, Written by James P. Dildine, 1999.

Borrowed Code from All-over-the-place

 

Social Media Links:

Additional navigation options:

1994-2016 MSTE | 505 East Green St., Suite 102, Champaign, IL 61820 | (217) 244-7486