about a polygon if all the vertices of the polygon lie on the circumference. The length of the circumference C of a circle is equal to π(see pi) times twice the radius distance r, or C=2πr. The area A bounded by a circle is given by A=πr2. Greek geometry left many unsolved problems about circles, including the problem of squaring the circle, i.e., constructing a square with an area equal to that of a given circle, using only a straight edge pass; it was finally proved impossible in the late 19th cent. (see geometric problems of antiquity). In modern mathematics the circle is the basis for such theories as inversive geometry and certain non-Euclidean geometries. The circle figures significantly in many cultures. In religion and art it frequently symbolizes heaven, eternity, or the universe.
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