How many ways are there to prove the Pythagorean theorem?



In a right-angle triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse. This theorem is one of the most basic and fundaments rules in geometry. It is made use while making stable buildings and GPS coordinates.

This theory is names after the Greek philosopher and mathematician from the 6th century B.C., known as – Pythagoras.


Although in the modern day we know Pythagoras to be the father of the theory. But it existed way before he did in the 1800 B.C. A tablet with a list of 15 sets of numbers was found from the Babylonia period. These sets of number were in concurrence with the modern-day Pythagoras theorem. It is also believed that Egyptians used the number 3, 4 and 5 to make square corners. Which is you take note of the converse of the theorem makes for a right-angled triangle, making those number to form a corner of the square which is right angled. The earliest presence of this theory if found with the Indian mathematical inscriptions which date way back to the 800 and 600 B.C. these texts state that of a rope is stretched through the diagonal of the square, it will result it formation of a square which is twice as large as the original square. This can also be taken from the Pythagoras theorem that we use today.


  1. The rearrangement – attributed by Pythagoras himself. Taking four identical right-angle triangles with “a” and “b” sides and the hypotenuse as “c”. rearrange them in such a manner that these triangles for a tilted square within them. And then rearrange them in manner that empty spaces make for the “b” and “a” side. The square of the first image will be equivalent to the sum of squares of the second image.
  2. Euclid and Young Einstein – both of them at different periods in time confirms that if the right-angled triangle was to be dived in two halves, the corresponding angles would also confirm the theory.
  3. Tessellation – repetitive geometric pattern also confirms this theory to be true.
  4. Turntable experiment – this one can be done by one’s self. Place three square boxes of each side of the right-angled triangle and place it on a turntable. Now fill the largest square with water, turn the table around and see how the other two squares get filled perfectly with water.

The theory can be proved in more than 350 ways to this date, and there are more proofs to be discovered to prove this particular theory.

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