You have a special eight-bladed pizza cutter. All you do is pick a point on the pizza, and the device cuts out eight straight lines from that point to the circumference of the pizza, separated by equal 45 degree angles.

You and your friend just bought a pizza and would like to have four slices of pizza each. Your friend tells you that you can make the cut using your device, using any center point you would like. After the cuts have been made, the two of you will eat alternate slices (so that nobody eats two adjacent slices).

How much of the pizza can you end up with?

(In reply to re(2): thoughts -- Somewhat messy solution by Richard)

Corrections: The final formula of my previous post should read

cos(2*X) + 2*[cos(X)]*sqrt((.5*cos(2*X))^2 + a^2- .5) + a^2. 

Also, it is (r^2)/2 that when integrated gives the area, and not r^2 itself.

These corrections do not affect the subsequent reasoning or the conclusion.

Edited on February 11, 2005, 2:38 am

Posted by Richard on 2005-02-09 18:21:00