# My Favourite Proof of Pythagoras’ Theorem

## A proof of the most remarkable Theorem in Maths

3 min readMay 1, 2024

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Pythagoras’s Theorem is a theorem that anyone past about the age of fourteen has learned at some point in their lives. The first Proof of it was created over two thousand years ago and has no exact date. But even though many consider it so simple and essential, I believe there is an intrinsic beauty in it that is unmatched by any other theorem in mathematics. Here, I will explain my favourite Proof of it, which I feel does its beauty justice.

## What Is Pythagoras’ Theorem

For those of you who have, by some miracle, forgotten this wonder, I shall state it here:

It is a formula that links the lengths of the sides of a right-angled triangle where C is the hypotenuse (The side opposite the right angle):

It is used often in many different areas of life, from films to architecture, and has become a staple of mathematics. This title is well-earned, and I am here today to share that beauty again.

## The Proof

This Proof starts by creating three copies of the Triangle and scaling them by different amounts. One by A, one by B and one C, then laying them against each other as in the diagram below. Then, since some side lengths are shared:

Here, we can look at some of the angles. Two of the corners are 90 degrees since they were original right angles, but the other two are made of the sum of the other two angles. For those who need to know, there is one other thing. That is the sum of angles in a triangle of 180 degrees. This gives if one angle is 90 degrees:

This proves that the other two angles are also 90 degrees, and the line at the bottom is right! Thus, what is the whole shape?

A rectangle!

And opposite sides of a rectangle are equal, so:

Credit for this proof goes to Geoffrey Margrave.

## Conclusion

Pythagoras’ Theorem is a fantastic freak of maths that pops out of Euclidean geometry. It has captivated mathematicians for thousands of years, and its number of proofs will surely keep rowing. And I encourage you to try and think of a different evidence of it, then check if it is already known. Because you may well have a new wonder on your hands. And as always,

Have fun, and never stop puzzling.

## Sources

https://www.cut-the-knot.org/pythagoras/proof41.shtml

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I have three Passions : Maths, Maths, Maths. Are these yours?