Trawling Thursday - Pythagoras

Pythagoras (or the Pythagoreans) discovered square numbers. 

The most common method for calculating the square root by hand is known as the "Babylonian method". It involves a simple algorithm, which results in a number closer to the actual square root each time it is repeated. To find r, the square root of a real number x:

Start with any positive start value, call this r.
Find the average of r and x/r; call this r2
Now find the average of r2 and x/r2; call this r3
Now find the average of r3 and x/r3; call this r4

Repeat these steps  until the two values  are as close as desired; that is the square root.  The closer they are the more accurate the final answer.

You have to love maths!

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