When two pieces of paper are stacked one atop the other, each point on the top piece sits directly above its matching point on the bottom piece. Now, crumple the top piece of paper into a ball and throw it back onto the bottom piece. Astoundingly, there is sure to still be at least one point in that top crumpled piece sitting directly above its matching point on the bottom! Or, take two maps of the U.S., one smaller than the other. Toss the small map somewhere onto the large map and you’ll be sure to find one point in the U.S. in exactly the same spot on both maps. And watch out when you stir your morning drink – in an ideal mathematical world, at least one point of liquid is sure to return to exactly the same location where it was before stirring! Let’s have fun playing with clever “ABC triangles” to find these freaky fixed points!

This program is recommended for middle schoolers and high schoolers.

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