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September
2000, Amsterdam - Projects
- Norway
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Tanja Brown (16)
School: Nesbru videreg†ende skole
Hobbies: travelling, playing piano, skiing, cooking and
dancing
Career intention: computer engineer
E-mail: tanja114@yahoo.com
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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.
http://www.unge-forskere.no/konkurransen/kuf2000/prosjekt/00_06.html
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