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The shape of an egg is approximately half of each of a prolate (long) and a roughly spherical (potentially even slightly oblate/short) ellipsoid joined at the equator, sharing a principal axis of rotational symmetry, as illustrated above.
The concept was introduced by Leonhard Euler in his 1765 book Theoria motus corporum solidorum seu rigidorum; he discussed the moment of inertia and many related concepts, such as the principal axis of inertia.