The Pythagorean relationship is much more than some theoretical postulate for calculating the lengths of sides on a right triangle. It can be used for so much more meaningful applications, such as astronomy, architecture, law enforcement, etc. This relationship is so much more significant than we often this it is. It is something that we can use.

The Pythagorean theorem has significance in many fields within and without mathematics. The examples of application are a testament of the significance of this theorem.

Although Pythagoras was disturbed by the fact that his theorem yielded irrational numbers, this discovery is important for the rest of the mathematical world. Irrational numbers are able to further understanding in geometry and calculus, especially when discussing finance.

The Pythagorean theorem represents a special case considered in Fermat’s Last Theorem. xⁿ + yⁿ = zⁿ doesn’t have any integer solutions, x,y,z, not equal to 0, where n>2. Although Fermat claimed to have proven this in his lifetime, his proof has been lost and it was not proven until 1994.