Pythagoras' Theorem

1. The theory: In a right angled triangle: the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

2. Although he is credited with the discovery of the famous theorem, it is not possible to tell if Pythagoras is the actual author. The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. Unfortunately, this vow of secrecy prevented an important mathematical idea from being made public.

2.1. History The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.?-500 B.C.?), who was perhaps the first to offer a proof of the theorem.

3. What is it?

4. Applications of Pythagoras' Theorem

5. Converse of Pythagoras' Theorem

6. Proof

6.1. Proof #1: Algebra

6.1.1. In the diagram, there are 4 right-angled triangles. To find out if a^2 + b^2 = c^2, we will find out the area of the different shapes.

6.1.2. The big square has an area of (a+b)^2.

6.1.3. The yellow square has an area of c^2.

6.1.4. The 4 triangles have an area of 2ab.

6.1.5. Adding the area of the yellow square and the 4 triangles would give us the area of the big square. Thus, 2ab + c^2 = (a+b)^2.

6.1.6. As we simplify this equation, it simplifies to a^2 + b^2 = c^2. Thus, we can conclude that the Pythagoras Theorem is accurate.