Pythagorean Triples
If a right triangle has integer side lengths a, b, c (necessarily satisfying the Pythagorean theorem a2+b2=c2), then (a,b,c) is known as a Pythagorean triple. As Martin (1875) describes, the Pell numbers can be used to form Pythagorean triples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles. Each such triple has the form
The sequence of Pythagorean triples formed in this way is
- (4,3,5), (20,21,29), (120,119,169), (696,697,985), ....
Read more about this topic: Pell Number
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