Geometry


	In my three years at Good Counsel, I only taught an Applied Geometry class one year. I don’t have a good collection for geometry, but here are a few. I intend to add more by and by. Feel free to send your favorite Geometry problems, and if I like them I’ll post them and credit you.


	Mr. Thompson is making a cake from a mix. The instructions on the box say to bake it for 25 minutes if using a 9-inch square pan, or for 30 minutes if using an 8-inch square pan. Unfortunately, Mr. Thompson (a bachelor) only has a 9-inch round pan. (It all tastes the same anyway.) How long should he bake the cake? Explain why and show your work.


	A builder has been asked for a price to put down a concrete sidewalk surrounding a swimming pool shaped like the trapezoid shown (lengths in feet). The sidewalk is to cover every point within 12 feet of the edge of the pool, and no point more than 12 feet from the edge of the pool. What will be the area of the sidewalk?


	An interesting bit of combinatorial geometry concerns self-surrounding tiles that will not cover the entire plane. An unsolved problem: With how many layers can a tile surround itself completely, and still be unable to tile the entire plane?


	Questions, corrections, comments: Send me e-mail at markthom@flash.net


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