The Pythagorean Theorem is likely one of the most widely known theorems in all of math. It states that for any right triangle, the sum of the squares of its sides are equal to the square of its hypotenus.

$$a^2+b^2=c^2$$

The theorem is also popular for there being numerous different ways to prove that it is true. It is popularly cited that there are over 350 unique proofs of the theorem, but the exact number varies up to 600.

Pythagorean Triple¶

A pythagorean triple is a set of three positive integers which satisfy the condition $a^2 + b^2 = c^2$.

$$\text{Pythagorean Triples} = \left\{a,b,c \in\Bbb Z^+\ |\ a^2+b^2=c^2\right\}$$

The smallest and most common example of a triple is $(3, 4, 5)$, but arbitrary triples can be generated with the use of Euclid’s formula.

Sources¶

• Proofs of the Pythagorean Theorem. Brilliant.org. Retrieved 19:05, August 9, 2026, from https://brilliant.org/wiki/proofs-of-the-pythagorean-theorem/
• https://jwilson.coe.uga.edu/emat6680su06/deitz/Geometry%20Presentation/Geometrypresentation.html