# The Pythagorean Theorem (Essay Sample)

IT is basically about the proof and application of THE Pythagorean Theorem

source..The Theorem of Pythagorean

A right-angled triangle has the relationship of its sides usually shown by the theorem of Pythagoras’s. This theorem is also called the theorem of Pythagorean where the squares of the shorter lengths of the triangle when summed is equal to the squared hypotenuse (Weisstein, 2006). This relationship is shown by use of an equation which is shown below. The two short sides length of the triangle and the hypotenuse are denoted by the letters a, b, and c respectively. Below is the drawing of the triangle and its equation for lengths.

22383751790700

ac

b

a2+b2=c2

Proofs of the Pythagorean Theorem

There are several proofs that show this theorem which are explained below;

* Rearrangement and dissection proof

This proof is usually the opposite of Einstein’s proof which is described. Inside a square, four triangles that are right-angled are moved forming two squares. When they are moved again, they form one square as it drawn below. In forming of the two squares first, the areas of the squares are a2and b2 whereas the other one is c2.

* Algebraic Theorem

Four right-angle triangles are used in this proof where the four triangles are arranged inside a square. The small square dimension is (b-a) by (b-a) whereas the bigger one is c by c as drawn in the figure below;

* Einstein’s proof

This proof shows a right-angled triangle being dissected without moving any side of the right-angled triangle.

* Similar triangles proof

Here two similar triangles no matter the size of the triangles are used in this proof. This proof indicates that the ratio of any two triangles that are similar and are right-angled is usually same.

Applications of Pythagoras Theorem

The Pythagoras theorem is used in various activities in the real life. Applications of this theorem in real life are given below:

This theorem is applied in finding the shortest distance in navigation that is two-dimensional. The two triangle’s legs are the two distances where

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