This idea lets you construct a 60 degree angle at a point A with just compass and straight edge. It's pretty simple.

- Make a line starting at A, and extend it to B.
- Open your compass to some distance smaller than AB.
- Put the compass point at A.
- Draw a small arc which intersects AB. Call the point at which it crosses C.
- Put the compass point at C.
- Draw a circle with the compass.
- Put the compass point at A.
- Draw an arc which crosses the circle. Call the point where it crosses D.
- Draw the straight line AD. Bingo!

This works because you have just defined three points (A, C and D) of an equilateral

triangle!