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Katzengold: Pyrite, Plato, and a Polynomial
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Katzengold: Pyrite, Plato, and a Polynomial
What are the similarities of the mineral pyrite, the dodecahedron as the fifth Platonic solid, and a polynomial of degree 16? This paper explores this connection by using the free software SURFER of the IMAGINARY open mathematics platform, which leads to fascinating pictures displaying transformations from a cube to a dodecahedron, to a rhombic dodecahedron, and to an octahedron, using a single formula. A survey on the ideas and the mathematics behind these visualizations is given. In fact, everyone can explore and modify these forms in real time using the SURFER software. Moreover, the authors have created a short movie, demonstrating the simple geometric beauty.
Mathematical subjects
Algebra and Number Theory
Didactics and Education
Geometry and Topology
Connections to other fields
Chemistry and Earth Science
Reflections on Mathematics
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English
Katzengold: Pyrite, Plato, and a Polynomial
German
Katzengold: Pyrit, Platon und ein Polynom
More general background material
Mathematical subjects
Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics
Connections to other fields
Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics