themathkid: 1. Take a circle and draw some points on the boundary. For every point you draw, you mus
themathkid: 1. Take a circle and draw some points on the boundary. For every point you draw, you must also draw its antipode (point on the opposite side of the circle). 2. Draw some points in the interior wherever you want. 3. Label the points either +1, -1, +2, or -2 as you wish. The only stipulation is that antipodes must have opposite sign. 4. Draw triangles however you want without crossing lines. Tucker’s Lemma says that you will ALWAYS end up with at least one line that has endpoints of either +1 and -1 or +2 and -2. Try it! More info and proof here. -- source link