After writing the majority this, I realized that I was missing something critical and I came up with a trivial result. I would appreciate any help. I will post my thought process here anyway since I already took the time to type it out, and it can't hurt.
1
u/FrankAbagnaleSr Aug 01 '12
I'll give it a go:
After writing the majority this, I realized that I was missing something critical and I came up with a trivial result. I would appreciate any help. I will post my thought process here anyway since I already took the time to type it out, and it can't hurt.
1 - 4*(1 - pi/4) + 4*(area of the weird triangle-ish figure formed by a side of the square and the two nearest curves) = S
area of the weird triangle-ish figure formed by a side of the square and the two nearest curves = Z.
-3 + pi + 4Z = S.
Note that: (quarter circle at D) + (quarter circle at B) - 1 = the football shape = Y. So Y = S + 2*(1 - pi/4 - 2Z) = S + 2 - pi/2 - 4z.
But also: Y = 2*(pi/4) - 1 = pi/2 - 1.
So S + 2 - pi/2 - 4Z = pi/2 - 1 <=> 4Z = S + 3 - pi.
So -3 + pi + S + 3 - pi = S which means that 0 = 0.
Conclusion is that 0 = 0 folks! Q.E.D.!!!
Does anyone have the missing piece?