mathworld.wolfram.com

Lemon Surface -- from Wolfram MathWorld

️Weisstein, Eric W.

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld

lemon

LemonCrossSection

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

z_+/-=+/-sqrt(R^2-(x+r)^2)

(1)

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.

Lemons

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

a^4(x^2+z^2)+(y-a)^3y^3=0

(2)

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

x^2-y^3z^3=0,

(3)

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

V_(citrus)=1/(140)pia^3,

(4)

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]

(5)

for a uniform density solid citrus with mass .

See also

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

Explore with Wolfram|Alpha

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." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemonSurface.html

Subject classifications