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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 Java 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
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Calculator Programs, Written by James
P. Dildine, 1999.
Borrowed Code from All-over-the-place
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Last Revised: 10/23/01