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Figure This!

According to the 1999 Guinness Book of Records, the world’s largest cake was prepared by EarthGrains Bakery to celebrate the centennial of Fort Payne, Alabama in 1989. Shaped like the state, it weighed a little more than 58 tons and used 16,209 pounds of frosting.

The Italian mathematician Francesco Bonaventura Cavalieri (1598–1647) developed a theorem that states if two three-dimensional solids have the same height and all cross-sections of the solid parallel to the base and at equal distances from the bases have equal areas, then the solids have the same volume.

If a cake is square and of the same height everywhere, then you can divide it into five shares of equal area using the idea behind the following drawing.

The square is separated into four triangles and rearranged as shown. If the sum of the bottoms of the triangles on the right is cut into five equal parts, then by connecting the tops of the triangles to the cuts on the bottom, there are 5 equal servings.




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