Lemon Surface


A surface of revolution defined by Kepler. It consists of less than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of the upper and lower boundaries in the xz plane are


for R>r and x in [-(R-r),R-r]. The cross section of a lemon is a lens. The lemon is the inside surface of a spindle torus. The American football is shaped like a lemon.


Two other lemon-shaped surfaces are given by the sextic surface


called the "citrus" (or zitrus) surface by Hauser (left figure), and the sextic surface


whose upper and lower portions resemble two halves of a lemon, called the limão surface by Hauser (right figure).

The citrus surface had bounding box ((-a/8,a/8),(0,a),(-a/8,a/8)), centroid at (0,a/2,0), volume


and a moment of inertia tensor

 I=[(1445)/(5148)Ma^2 0 0; 0 5/(858)Ma^2 0; 0 0 (1445)/(5148)Ma^2]

for a uniform density solid citrus with mass M.

See also

Apple Surface, Lens, Oval, Prolate Spheroid, Spindle Torus

Explore with Wolfram|Alpha


Hauser, H. "Gallery of Singular Algebraic Surfaces: Zitrus." "Classic Surfaces from Differential Geometry: Football/Barrel."

Cite this as:

Weisstein, Eric W. "Lemon Surface." From MathWorld--A Wolfram Web Resource.

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