Pythagorean theorem: right triangle calculator
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².
History of the theorem
Although named after Pythagoras of Samos (6th century BC), the theorem was known to Babylonians and Egyptians over 1,000 years earlier. More than 370 different proofs have been found. One of the most elegant uses the area of squares built on each side of the triangle.
Practical applications
- Construction: verifying a corner is perfectly square (3-4-5 rule).
- Navigation: calculating straight-line distances on 2D maps.
- Computing: Euclidean distance between two points on a screen.
- Architecture: calculating lengths of diagonal beams.
- GPS: trilateration to determine geographic position.
Pythagorean triples
Sets of three integers satisfying a² + b² = c². Most known: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25). Any multiple of a triple is also a triple: (6, 8, 10), (9, 12, 15), etc.