WOLFRAM|DEMONSTRATIONS PROJECT

Twin Pythagorean Triples

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set of triples
1
The Pythagorean triples: leg-hypotenuse twin triples
This is a twin Pythagorean triple: {3,4,5}
and this is the next one: {5,12,13}.
For each such pair,
the sum of the smaller legs: 3 + 5 = 8
equals the difference of the larger legs: 12 - 4 = 8
and is also equal to the difference of the hypotenuses: 13 - 5 = 8.
The sum of the three sides is always an even number.
This is even: 3 + 4 + 5 = 12,
and this is even: 5 + 12 + 13 = 30.
The angle formed by the smaller side and the hypotenuse measures:
θ
1
= 0.927295 rad. = 53.1301°.
The angle formed by the bigger side and the hypotenuse measures:
θ
2
= 0.643501 rad. = 36.8699°.
A twin Pythagorean triple is a Pythagorean triple for which two values are consecutive. This Demonstration generates 100,000 twin Pythagorean triples, calculating two at a time.