So after that last problem I got to thinking that the area between a circle and its bounding or contained square would be potentially useful to know. Really. It just seemed cool. Only problem is that every use for it I could think of I could think of other ways to get there. Grrrr. Is this really cool – or is it the mathematical equivalent of carrying around a small dog in a shoulder bag?
Finally I have some time to work through daily problems again. Worked this one last week and forgot to write it up.
When I saw this problem I just saw the trigonometry solution and it blinded me to the symmetry. I guess math is good at showing how what we already know can blind us to the better paths.
So why do mathematicians suck? Well that seemed politer for Konrad than saying he sucks – I worked on this problem for a while and just did not see it. He saw the answer before I was finished describing the problem. So I guess I am the one who sucks, – apologies to mathematicians everywhere.
The pythagorean theorem states that for a right triangle the sum of the squares of the opposite and adjacent sides is equal to the square of the hypotenuse. I used a graphical proof to prove this theorem.
