Expository essay
The Cesàro Method for Spherical Trigonometry
Second-year undergraduate essay.
15 pagesRevised in August 2026
Converted from LaTeX to Typst in 2026 and lightly edited for language, notation, presentation, and minor corrections.
Abstract
This essay presents the Cesàro method for spherical trigonometry. After a brief introduction to spherical geometry, we establish the circle-preserving and conformal properties of stereographic projection. We then use stereographic projection to associate a planar triangle with a spherical triangle and apply Euclidean trigonometry to derive the spherical law of cosines, two of Delambre’s analogies, and one of Napier’s analogies.