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

Stephan Klaus ()
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Stephan Klaus: Mathematisches Forschungsinstitut Oberwolfach

A chapter in Singularities and Computer Algebra, 2017, pp 161-172 from Springer

Abstract: 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; 14J25; 14Q10; 51N10; 52B10; 55R80; 57M25; 57N05; 57N35 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-28829-1_8

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