Project week

Homepage

Algebraic surfaces with symmetries

In 2011 I presented a project for pre-university students together with Josef Schicho. The theme of this project week was: algebraic surfaces with symmetries.

The representation of curves and surfaces by algebraic equations is often used for geometric modeling. For artistic and aesthetic reasons one could wish that these curves and surfaces have symmetric properties. Mathematically, symmetries can be described by groups of figures. Which groups are possible? And how to find equations such that the corresponding figure has a given symmetry group?

See the project week homepage for more information.

Picture

Here are some lecture notes (comments are welcome).

Below we see some symmetric algebraic curves and surfaces that were constructed by the students using Sage and Mathematica.

Picture Picture Picture Picture
Picture Picture Picture Picture