How does one give a proof that is
- short; and
- strictly within the bounds of secondary-school geometry
that the stereographic projection
- is conformal; and
- maps circles to circles?
2026-03-29 22:06:44.1774822004
Elementary arguments concerning the stereographic projection
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I'm not sure what is in the post by TheoBromine, it says I need plugins to see all the media on the page. But a full and very careful proof, with five figures, is in Geometry and the Imagination by David Hilbert and Stephan Cohn-Vossen, translated by P. Nemenyi, see AMAZON AND GIGGLEBOOKS on pages 248-251. Also available reprinted by the AMS in 1998 or so.
P.S. Giggle let me see all of pages 248-251.