Visual geometry

If you’re puzzled by the title of this post, allow me to explain.

A natural reaction would be “Isn’t geometry intrinsically visual?” Indeed, geometry is motivated by things we can visualize. But modern developments of geometry have become heavy with formal machinery, so much so that one could reasonably ask “What happened to the geometry?”

Tristan Needham has a new book entitled Visual Differential Geometry and Forms that aims to put the geometry back into a first course on differential geometry. I expect it’s a good read based on having read his previous book Visual Complex Analysis.

I just got a review copy in the mail, and flipping through the book I can see that it lives up to its title. It has lots of illustrations, just as you’d expect from a book on differential geometry if you hadn’t taken courses in the subject.