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What are the uses of square root spiral?


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Solution

Find the uses of square root spiral.

Theodora's' spiral is often known as the square root spiral or the Pythagorean spiral. It's a spiral made up of consecutive right triangles.

Every triangle contains a single side length, reflecting the a2 of the Pythagorean theorem, with the other sides filling in the gaps for the b2andc2 in the theorem.

The spiral was used by Theodora to demonstrate that all non-square numbers between 3and 17 are irrational.

The original spiral terminates at 17 since it is the last hypotenuse before covering the remainder of the picture.

Furthermore, Erich Teuffel demonstrated long later that no two hypotenuses will ever intersect irrespective of how deep the spiral runs. All side lengths of 1 would be stretched into a line that will never pass into any of the figure's remaining vertices.

Hence, a spiral has been used by Theodora to argue that all non-square numbers 3-17are irrational.


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