September 2000, Amsterdam - Projects - Norway

Tanja Brown (16)
School: Nesbru videreg†ende skole
Hobbies: travelling, playing piano, skiing, cooking and dancing
Career intention: computer engineer

A study of projections of surfaces
In my project I studied the patterns achieved when mapping singularities of various surfaces from one plane to another. To understand what a singularity is, consider the following example: If a person's face is drawn on a sheet of paper, it is as if the three-dimensional surface of the face is being projected onto a two-dimensional piece of paper. The corresponding outline of the face represents the singularities of the face, so to speak. Mathematically, singular points are defined as points where the partial derivate dz/dx is equal to zero. Whitney's Theorem states that there are only two stable patterns when mapping singularities: folds and cusps. I designed a computer program that maps various functions and I studied the resulting patterns of singularities, especially those relating to Whitney's Theorem. .