Sunset Geometry (2016)

Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake. Vanderbei’s analysis is an elegant and subtle exercise in classical trigonometry. In this post, I would like to present an alternative analysis in a different language: Geometric Algebra. I believe that geometric algebra is a more powerful system for formulating and solving trigonometry problems than the classical “lengths and angles” approach, and it deserves to be better known. Vanderbei’s sunset problem is simple to understand and challenging to solve, so it makes a nice benchmark. Here’s Vanderbei’s sunset problem. If the earth was flat, photographs of the sun setting over water would look like this: Notice that the reflection dips just as far below the horizon as the sun peaks above it. Actual photographs of the sun setting over calm water (like Vanderbei’s ⊕ Update: I should have been more ca ... Read full article.