Robert Vanderbei presents an elegant method to calculate the radius of the earth using a photo of a sunset over a calm lake, challenging to solve yet visually straightforward. The classical trigonometry approach is compared to a more powerful Geometric Algebra method by exploring unit directions rather than angles. The mathematical analysis involves vector equations and geometric conditions, all culminating in the derivation of the earth’s radius based on known angles and camera height above the water. Geometric algebra introduces unique tools like the geometric product, allowing for efficient solutions to vector equations and transitive relationships. Vanderbei’s sunset problem serves as a practical application of these advanced mathematical concepts.
https://www.shapeoperator.com/2016/12/12/sunset-geometry/