Math is …. Beautiful?

Aug 07, 2013 • Math

If asked to finish the sentence “Math is…”, one could easily guess what many students would say.

Hard.
Stupid.
The worst.

But could the sentence really end with “beautiful”?

The New York Times Crossword Blog recently featured a math puzzle by Daniel Finkel of Math for Love, a Seattle-based math duo dedicated to helping students and teachers fall in love with the beauty of mathematics.

The challenge? The 10-Point Angle Maze:

“Consider 10 points equally spaced around a circle, labeled zero to nine as pictured.

Starting and ending at zero, your goal is to draw a continuous straight-line path that hits every point without creating any acute or right angles at those points.

For example, one answer is to make a regular 10-gon (or decagon). But it turns out there’s one more way to do it. Can you find it? (to clarify, you may cross your own path, and you need to make obtuse angles only at the original 10 points: New vertices created by overlapping lines don’t count. We’ll consider solutions to be unchanged under reflections. Aside from starting and ending at zero, you can’t hit the same point twice or retrace your own path). If you can find the second solution, can you prove there are no more?”

Read about how Dr. Finkel came up with the Angle Maze concept here.
And let us know if you are able to solve the puzzle! How long did it take you?