# Can a square ever have 5 sides

## Pythagorean theorem and its inversion

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The Pythagorean theorem and its inversion Here you can find out what the Pythagorean theorem and its inversion mean and what a Pythagorean number triplet is.

### The reverse of the Pythagorean theorem

A right angle can be easily staked out in the field. To do this, take a piece of string and divide it into 12 equal parts using 11 knots. With this string you can create a triangle with sides 3, 4 and 5, because 3 + 4 + 5 = 12. The result is a right angle. That this “trick” works does not follow from the Pythagorean theorem, but from its reversal. This inversion says: If in a triangle, then the triangle is right-angled, with the right-angle being the side with the length opposite. So you can use the side lengths of a triangle to check whether it is a right triangle.

Reversal of the Pythagorean theorem: If in a triangle with the side lengths, and the equation holds, then the triangle is right-angled, with the right angle facing the side with the length.

If you want to check a triangle for perpendicularity, only the longest of the three sides can be used as a hypotenuse.

### Pythagorean triplets

Three natural numbers,, that satisfy the equation are called (triples because they are three numbers). The triple (,,) is such a Pythagorean number triplet.

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