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What is the 3-D shape of a football called? A soccer ball is circular and called a sphere. A football is an ellipse but what do you call the 3-D shape called?

A football is not really an ellipse. The equation of the projection onto the x/y plane of an ellipse of revolution is (x/a)^2 +(x/b)^2 = 1. where 'a' and 'b' are the semi-major and semi-minor axes, respectively. The foot ball is too "pointed" on the ends to be an ellipse according to the definition above. The general name for objects that have an axis of symmetry, like a football ignoring the sewing and the laces, is an oval of revolution.

There are methods for generating analytical equations of such geometric figures, but space does not permit that discussion in this forum.

Vince Calder


The three-dimensional figure that best fits a football is an ellipsoid. An ellipsoid is formed by rotating an ellipse around one of its two axes. You can get something like a football or something like a flying saucer, depending on which axis you choose.

Dr. Ken Mellendorf
Illinois Central College

An Americal football is a prolate spheroid. This means that its axis of symmetry is longer than its other axes. Am M&M candy, on the other hand, is an oblate spheroid. Its axis of symmetry is shorter than its other axes.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois


Thanks to David H.

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