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?