Offering equal time to equations

Over the years, this site has accumulated enough pages about mathematical topics to give them their own section. The level of what you'll find here varies from high-school algebra to advanced undergraduate work. I try to approach subjects visually, so expect pictures.

The Cone

The formula for the cone's surface area can be derived with basic algebra. Finding its geodesics was fun.

The Torus

College courses in differential geometry and general relativity got me wondering about the torus's curvature, shape operator, and geodesics, as well as parallel transport on the torus, so I took a look at them. These pages are summaries; full results are available as a PDF.


Using color can make the fourth dimension surprisingly concrete.

Plotting triplets offers a way to display three independent variables in a two-dimensional chart.


For laughs, I expanded a component of a Riemann tensor of a 4-space in terms of the metric tensor.

Last updated 1 May 2006
All contents ©2004 Mark L. Irons