Lemon Surface (original) (raw)
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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 
plane are
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for 
and ![x in [-(R-r),R-r]](https://mathworld.wolfram.com/images/equations/LemonSurface/Inline3.svg)
. 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
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called the "citrus" (or zitrus) surface by Hauser (left figure), and thesextic surface
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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 
, centroid at 
, volume
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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]](https://mathworld.wolfram.com/images/equations/LemonSurface/NumberedEquation5.svg) |
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for a uniform density solid citrus with mass 
.
See also
Apple Surface, Lens, Oval, Prolate Spheroid,Spindle Torus
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References
Hauser, H. "Gallery of Singular Algebraic Surfaces: Zitrus." https://homepage.univie.ac.at/herwig.hauser/gallery.html.JavaView. "Classic Surfaces from Differential Geometry: Football/Barrel." http://www-sfb288.math.tu-berlin.de/vgp/javaview/demo/surface/common/PaSurface_FootballBarrel.html.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Lemon Surface." FromMathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LemonSurface.html