TOPICS
Search

Cone Net


ConeGridsConeNets

The mapping of a grid of regularly ruled squares onto a cone with no overlap or misalignment. Cone nets are possible for vertex angles of 90 degrees, 180 degrees, and 270 degrees, where the dark edges in the upper diagrams above are joined. Beautiful photographs of cone net models (lower diagrams above) are presented in Steinhaus (1999). The transformation from a point (x,y) in the grid plane to a point (x^',y^',z^') on the cone is given by

x^'=rncos(theta/n)
(1)
y^'=rnsin(theta/n)
(2)
z^'=(1-r)h,
(3)

where n=1/4, 1/2, or 3/4 is the fraction of a circle forming the base, and

h=sqrt(1-n^2)
(4)
theta=tan^(-1)(y/x)
(5)
r=sqrt(x^2+y^2).
(6)

See also

Cone, Sphericon

Explore with Wolfram|Alpha

References

Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 224-228, 1999.

Referenced on Wolfram|Alpha

Cone Net

Cite this as:

Weisstein, Eric W. "Cone Net." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConeNet.html

Subject classifications