Stereographic Projection of a Coffin Problem

Hubert Shutrick came up with an elegant solution to one of the coffin problems:

One solution based on the idea of center of gravity (barycenter) appeared elsewhere.

Hubert Shutrick's solution draws on the conformality (angle preservation) propety of the stereographic projection.

Copyright © 1996-2009 Alexander Bogomolny

Stereographic projection converts the coffin problem into a problem in Euclidean geometry that is interesting in its own right. Since each vertex of the skew quadrilateral along with two adjacent tangency points defines a circle on the sphere by the plane of the sides that meet in the vertex; these four circles A, B, C, D can be projected down onto the plane and A is tangent to B is tangent to C is tangent to D is tangent to A (because, any successive two share a point but lie in different planes). Show that the points where they touch lie on a circle. It is not difficult to prove by just chasing angles but, of course, follows directly from the elegant solution of the original problem.

Stereographic Projection

• Stereographic Projection and Radical Axes
• Stereographic Projection and Inversion
• Stereographic Projection of a Coffin Problem
• Stereographic Projection - an Interactive Tool
• Objects distant and near

Copyright © 1996-2009 Alexander Bogomolny