Apple Surface
apple
AppleCrossSection
A surface of revolution defined by Kepler. It consists of more 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 x-z plane are
| z_+/-=+/-sqrt(R^2-(x-r)^2) |
(1)
|
for R>r and x in [-(r+R),r+R]. It is the outside surface of a spindle torus.
It is also a quartic surface given by Cartesian equation
| (r^2-R^2+x^2+y^2+z^2)^2=4r^2(x^2+y^2) |
(2)
|
or
| r^4-2r^2(R^2+x^2+y^2-z^2)+(-R^2+x^2+y^2+z^2)^2=0. |
(3)
|
See also
Bubble, Lemon Surface, Oblate Spheroid, Snake, Sphere-Sphere Intersection, Spindle TorusExplore with Wolfram|Alpha
WolframAlpha
Cite this as:
Weisstein, Eric W. "Apple Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AppleSurface.html