Shadow Problems

The work on this page was inspired by the following problem from a freshman Calculus course:
A street light is mounted at the top of a 15-ft tall pole. A man 6 feet tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is tip of his shadow moving when he is 40 ft from the pole?
Any calculus student should be able to solve this problem assuming the individual is walking Euclidean Space. My paper on Euclidean, Spherical and Hyperbolic Shadows addresses this problem in Spherical and Hyperbolic Geometry. This site contains some supporting computations and graphics. The paper is scheduled to appear in the March 2012 edition of The College Mathematics Journal The Mathematica notebook containing all computations in the paper can be found here. It also contains all the code which produced the pictures and animations. The notebook relies upon the following Mathematica packages:

I gave a shorter version of this talk at the Spotlight on Graduate Research Competition on February 17, 2009. Slides are here
I gave a talk on this at the Université de Sherbrooke on September 25, 2008. Slides with lots more pictures can be found here

Shadows on the Sphere

Stereographic projection of shadows on the Sphere

Shadows in the Hyperbolic Plane

Equidistant curves in each geometry

Last modified December 15, 2012. Back to EGL Homepage