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He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder. His tombstone is said to have had a figure of a sphere inscribed inside a cylinder and the 2:3 ratio of the volumes between them, the solution to the problem he considered his greatest achievement according to some...
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What makes them special is that even though many solid figures having all kinds of surfaces can be constructed, those which appear to be regularly formed are some of the most interesting to mathematicians. Five figures like those previously mentioned were discovered before Archimedes, and those include the tetrahedron, the cube, the octahedron, the dodecahedron, and finally the icosahedron...
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