Lemon (geometry)

The surface of revolution of the complementary arc of the same circle, through the same axis, is called an apple.

The lemon forms the boundary of a convex set, while its surrounding apple is non-convex.

[1][2] The ball in North American football has a shape resembling a geometric lemon.

However, although used with a related meaning in geometry, the term "football" is more commonly used to refer to a surface of revolution whose Gaussian curvature is positive and constant, formed from a more complicated curve than a circular arc.

[3] Alternatively, a football may refer to a more abstract orbifold, a surface modeled locally on a sphere except at two points.

The surface area is given by[5] The volume is given by These integrals can be evaluated analytically, giving The apple is generated by rotating an arc of half-angle