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Möbius Strips, Knots, Pentagons, Polyhedra, and the SURFER Software

  • Stephan KlausEmail author
Chapter

Abstract

The SURFER software for the visualization of real algebraic surfaces was developed from professional research software. It was adapted to the IMAGINARY exhibition of Oberwolfach under the direction of Gert-Martin Greuel in the Year of Mathematics in Germany 2008. As it is freely available and very easy to use also for nonexperts, it became one of the most successful public tools to visualize mathematical objects. Based on many discussions with Gert-Martin Greuel, the author used this software to give algebraic constructions and visualizations of some low-dimensional objects in geometry and topology. This has led to new connections and specific constructions for objects such as knots, moduli spaces of pentagons, and polyhedra.

Keywords

Algebraic variable elimination Cinquefoil knot Dodecahedron Icosahedron Möbius strip Octahedron Pentagon moduli space Pyrite Real algebraic surface Rhombic dodecahedron Spherical harmonics Torus knot Trefoil knot 

MSC:

14J25 14Q10 51N10 52B10 55R80 57M25 57N05 57N35 

Notes

Acknowledgements

I was introduced to the SURFER software by Gert-Martin Greuel in 2008, and I got interested immediately because of possible visualizations of two-dimensional topological objects. I would like to thank Gert-Martin cordially for all his advice and help with algebraic geometry and numerous discussions on mathematics. I learned from him the importance of raising public awareness for its beauty. This written version of my talk at the Pfalz-Akademie conference 2015 in honor of Gert-Martin Greuel gives a report on the surfaces and visualizations which I studied since 2008, emphasizing his influence to my work.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Mathematisches Forschungsinstitut OberwolfachOberwolfachGermany

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