You are at a restaurant. There are a total of three people(including you). Now you order a pizza and the trouble is that all three(including you) want equal parts. You have only a knife.
How do you cut the pizza in three equal parts?
EDIT for even edges
At the risk this is not the intended solution, but here goes.
We are assuming:
Cut a straight line from the center of the circle to the outer edge. where the line would extend to the other outer edge, don't cut the entire line, but make a marking cut on the outer edge. Now take your piece of string, and 'measure' the radius of pizza (along the cut you first made). Using said lenght, use that as a radius, from the 'marking cut' you made on the opposite side. You can use that to find two intersecting points with a circle radius r from the 'marking cut' point with the circles edge. Mark those two points with a small cut. Now just make straight cuts from both of those new 'marking cuts' to the center.
Why does this work?
Cosine(60) = 1/2. Basically, the perpendicular bisector of a line cuts it in half and is easy to construct. The second set of marking cuts have a cosine of 1/2 (half the radius compared to radius). 2x that angle makes a 120 degree angle between the parts, which is what you need to form a perfect three way split on a 360 degree circle.
Video of a similar method:
(but using measuring to spot the half, which I conveniently replaced with the 'use floss to create the perpendicular bisector' thingy): Youtube video
EDIT: This would also work if you think you have proficient eyesight to spot the middle of a line perfectly, and can but perfectly perpendicular without any assistance.
Different method then other answer, but works equally well using a piece of string / dental floss / whatever.
We are assuming:
From the center of the circle, use the string to 'copy' the radius of the pizza. Pick a random point on the other edge, make a marking cut. Use the string to find the intersections of a circle with radius r with the edge of the pizza (two such points), mark them with cuts. From one of the cuts, repeat the method, you'll find two points (the one you came from, and one new). Repeat two more times to find a total of 6 cuts. Then, cut in straight lines from center to cuts on the outside, each time skipping one of the cuts. You'll end up with 3 120 degree parts.
(not mine, found it on this page): link