Lemon (geometry)

In geometry, a lemon is a geometric shape that is constructed as the surface of revolution of a circular arc of angle less than half of a full circle rotated about an axis passing through the endpoints of the lens (or arc). The surface of revolution of the complementary arc of the same circle, through the same axis, is called an apple.

Half of a self-intersecting torus
A lemon

The apple and lemon together make up a self-crossing torus, the surface of revolution of the entire circle, with the apple as the outer shell of the torus and the lemon as its inner shell. The lemon forms the boundary of a convex set, while its surrounding apple is non-convex.[1][2]

North American football

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.[4]

See also

References
  1. Kripac, Jiri (February 1997), "A mechanism for persistently naming topological entities in history-based parametric solid models", Computer-Aided Design, 29 (2): 113–122, doi:10.1016/s0010-4485(96)00040-1
  2. Krivoshapko, S. N.; Ivanov, V. N. (2015), "Surfaces of Revolution", Encyclopedia of Analytical Surfaces, Springer International Publishing, pp. 99–158, doi:10.1007/978-3-319-11773-7_2
  3. Coombes, Kevin R.; Lipsman, Ronald L.; Rosenberg, Jonathan M. (1998), Multivariable Calculus and Mathematica, Springer New York, p. 128, doi:10.1007/978-1-4612-1698-8
  4. Borzellino, Joseph E. (1994), "Pinching theorems for teardrops and footballs of revolution", Bulletin of the Australian Mathematical Society, 49 (3): 353–364, doi:10.1017/S0004972700016464, MR 1274515
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