Unlocking Spherical Trigonometry with Quaternions

This article leverages the algebraic properties of quaternions to derive a 'master equation' for spherical trigonometry, elegantly proving the spherical law of cosines, the spherical law of sines, and Napier's rules. The author cleverly connects quaternions to the relationships between sides and angles of spherical triangles, using rotations and inner products to derive concise and elegant formulas. Applications to practical problems like calculating sunrise and sunset times are discussed, showcasing the power of quaternions in geometric problems.