Lemon (geometry)

In geometry, a lemon, sometimes called an ovoid of revolution, refers to a three-dimensional shape formed by rotating an arc of a circle less than a semicircle around an axis that does not intersect the arc. Specifically, imagine taking a circular arc shorter than 180 degrees and spinning it around a line situated outside the arc. The resulting solid will resemble a lemon in shape, hence the name.

The key characteristics are that it is a solid of revolution, derived from a circular arc, and possesses a pointed end where the arc is nearest the axis of revolution and a blunter end farthest from the axis of revolution. Unlike a sphere, which is generated by rotating a semicircle, the lemon's generating arc is less than a semicircle, leading to its distinctive, asymmetrical, ovoid form. The shape is entirely determined by the radius of the circle containing the arc, the angle subtended by the arc, and the distance from the center of the circle to the axis of revolution. Different combinations of these parameters will result in lemons of varying degrees of pointedness.