# Jean Constant - Sphere eversion

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.

## Eversion #1

The outlines of the eversion have been distorted and reconstructed as a wall relief to emphasize the paradox of interpreting a 3-dimensional problem in a two dimensional setting.

## Eversion #2

Denner’s original sketch was transferred into a 3D - polygon and 2D - vector based program to explore the original object and create a new self contained object.