applied mathemagics

The official regulation MLB home plate is mathematically impossible:

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle with a coincident isosceles triangle placed on one side) a "isosceles right pentagon."

However, specification of the shape of home plate, illustrated above, as specified by both the Major League Baseball Official Rules and the Little League rulebook (Kreutzer and Kerley 1990) is not physically realizable, since it requires the existence of a (12, 12, 17) right triangle, whereas

(Bradley 1996). More specifically, the standards require the existence of an isosceles right triangle with side lengths 8.5 inches and a hypotenuse of length 12 inches, which does not satisfy the Pythagorean theorem.