S. Smale  proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. Another eversion was devised by mathematician B. Morin and produced explicit algebraic equations describing the process. During the eversion, the surface must cross through itself transversally. On a given point, the tangent plane must various continuously. When these conditions are realized, the eversion of the sphere becomes possible.

R. Denner work was chosen to illustrate the challenge of converting a 3-dimensional isssue onto a 2-dimensional surface while preserving the integrity of the demonstration.