Abstract
In this chapter we introduce two geometric topics related to regular polygons and regular polyhedra. They illustrate a typical mathematical procedure: given a class of objects defined by an abstract property, we want to understand which “concrete” objects actually belong to the class, that is we want to “characterize” the class. This is the core idea which the reader is invited to think about. Besides this main theme, several other mathematical ideas will be presented, such as plane isoperimetric problems and topological properties of surfaces.
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Notes
- 1.
Recall that a subset A of the plane or of the space is said to be convex if for every pair of points P, Q ∈ A, the whole segment \(\overline{PQ}\) is contained in A.
- 2.
This proof is due to the French mathematician A. Cauchy (1789–1857), who discovered it at the age of 21.
Reference
Cuomo, S. (2000), Pappus of Alexandria and the mathematics of late antiquity. Cambridge: Cambridge University Press.
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Bramanti, M., Travaglini, G. (2018). Tiles, Polyhedra, and Characterizations. In: Studying Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-91355-1_18
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DOI: https://doi.org/10.1007/978-3-319-91355-1_18
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