File:Lexell's theorem in the hyperbolic plane (half-plane model).png

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Lexell's theorem: triangles of constant area on fixed base AB have their free vertex C along a small circle through points antipodal to A and B. In the half-plane model of hyperbolic geometry, antipodal points are outside the hyperbolic plane.

Summary[edit]

Description
English: Lexell's theorem: triangles of constant area on fixed base AB have their free vertex C along a small circle through points antipodal to A and B. In the half-plane model of hyperbolic geometry, antipodal points are outside the hyperbolic plane.
Date
Source Own work, plotted with Desmos https://www.desmos.com/geometry-beta/povdnwn9a2
Author Jacob Rus

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Date/TimeThumbnailDimensionsUserComment
current00:11, 9 July 2023Thumbnail for version as of 00:11, 9 July 20231,106 × 1,204 (276 KB)Jacobolus (talk | contribs)add antipodal hypercycle
22:03, 3 July 2023Thumbnail for version as of 22:03, 3 July 20231,116 × 1,214 (252 KB)Jacobolus (talk | contribs)add geodesic ("straight line") in purple
21:57, 3 July 2023Thumbnail for version as of 21:57, 3 July 20231,176 × 1,216 (248 KB)Jacobolus (talk | contribs)Uploaded own work with UploadWizard

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