Fractions, tilings, and geometry
Are there any rectangles whose perimeter and area have the same numerical value? Are there any rectangular boxes whose surface area and volume have the same numerical value? Can the plane be tiled with kites and chevrons? In how many ways can 1/2 be written as a sum of unit fractions? How are all of these questions related? We'll investigate these and other delights over the course of three weeks. No prior knowledge is assumed---the only prerequisite is a love of working on interesting problems.
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