Cutting, Gluing, Squeezing, and Twisting: Visual Design of Real Algebraic Surfaces

Stephan Klaus ()
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Stephan Klaus: Oberwolfach Research Institute for Mathematics

Chapter 29 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 863-877 from Springer

Abstract: Abstract The theory of real algebraic surfaces studies the connection between the algebraic properties of a polynomial p(x, y, z) in three real variables and the geometric and topological properties of its set of zeros in three-space. We give an overview on some methods how to create interesting real algebraic surfaces which are also looking nice from the esthetic viewpoint. The surfaces are visualized using the free SURFER software.

Keywords: Real algebraic surface, Variable elimination, Möbius strip, Trefoil knot, Octahedral symmetry, Polyhedron, Pentagon, Moduli space, Coordinate transformation, MSC: Primary 14-04, 14H45, 14H50, 14J17, 14P05, 14Q10, and 14Q30; Secondary 65D18, 68 U05, 97G60, 97G99, 97H30, and 97N80 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/978-3-319-57072-3_118

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