3-4-5
- Input
- a=3, b=4, c=5
- Expected output
- 9+16=25 ✓
Simplest primitive triple.
pythagorean triples
Pythagorean Triples
A Pythagorean triple (a, b, c) satisfies a²+b²=c² with a, b, c positive integers. They underpin many practical geometric constructions.
How to generate Pythagorean triples
- Euclid's formula generates primitive triples: for m > n > 0 coprime with m−n odd: a = m²−n², b = 2mn, c = m²+n². Example: m=2, n=1 → (3,4,5).
Classic triples
5-12-13
- Input
- a=5, b=12, c=13
- Expected output
- 25+144=169 ✓
Second primitive triple.
Full tool FAQ
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: c² = a² + b². Attributed to Greek mathematician Pythagoras (~570–495 BC).
Frequently asked questions
Are there infinitely many triples?
Yes. Euclid's formula generates infinitely many primitive triples, and any multiple of a triple is also a triple.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.