Hello everyone, if you didn't read my earlier post about how you can draw a few lines and a circle to calculate the square root of a number, take a moment to read it over HERE.
Now, for those that have read that post, have you figured out why it works? In this post, I'll give you the first of two solutions that I've found.
Solution 1, Pythagoras Theorem:
Looking at the image below, we are going to solve the basic Pythagoras Theorem for this triangle A2+B2=C2. All we must do now is express A, B, and C in terms of X (our known value) and Y.
The hypotenuse C is straightforward. This is simply the radius of the circle. We know that the diameter of the circle is X+1 so the radius is half of this (X+1)/2.
The leg along the diameter B is just a tiny bit more complicated. If you look at the first image, it’s one less than the radius. This works out to be (X-1)/2. If you want to see why this is the case, here you go:
Finally, the other leg is Y (that one was EASY!).
Putting all of this into the Pythagoras Equation and then solving for Y looks like this:
And there you have it. An elegant solution for what is, nowadays, a very simple problem!