Though the expression is odd, it caused me to stop focusing on the bout in the ring, and instead on the fun little geometry problem I concocted in the corner of my brain that loves math. Can you solve this puzzle?

__The square circle puzzle:__

Consider two shapes, one a square, the other a circle. Both shapes have the same area, individually. When the shapes are concentric, what ratio of their areas overlap (are shared)?

**The red portion of the concentric shapes is shared**

This is the sort of math problem I really enjoy: no numbers, as pure as can be. Whatever the answer, it is independent of the size of the shapes.

I have yet to sit down and attempt to solve the problem, but my gut feeling is that there are many ways to go about it. The 'obvious' way would be to use integration, but that seems hard due to the discontinuity. Which kind of coordinates would be best, polar or rectangular? I believe this can instead be solved without Calculus. Pythagorean level math should suffice. Again, that's just my gut feeling.

I will try to solve this without Calculus, and put up the solution to this (Part 2) within a couple of weeks. Give it your best shot. Oh, and if anyone knows the origin of the ridiculous 'square circle' expression, please leave it in a comment.

## No comments:

Post a Comment