The Pentagon Theorem in Miquelian Möbius Planes
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Date
2023-10-29
Publication Type
Journal Article
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Abstract
We give an algebraic proof of the Pentagon Theorem. The proof works in all Miquelian Möbius planes obtained from a separable quadratic field extension. In particular, the theorem holds in every finite Miquelian plane. The arguments also reveal that the five concyclic points in the Pentagon Theorem are either pairwise distinct or identical to one single point. We also identify five additional quintuples of points in the pentagon configuration which are concyclic.
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published
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Journal / series
Volume
16 (2)
Pages / Article No.
689 - 696
Publisher
Electronic Journal of Geometry
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Subject
Pentagon theorem; Möbius planes; Miquel planes