I was saddened to hear the news that Geoff Mess recently passed away, just a few days short of his 54th birthday. I first met Geoff as a beginning graduate student at Berkeley, in 1995; in fact, I believe he gave the first topology seminar I ever attended at Berkeley, on closed 3-manifolds which non-trivially cover themselves (the punchline is that there aren’t very many of them, and they could be classified 3,891 more words

## Tags » Hyperbolic Geometry

#### "The Heresy of Friar Travolo" now at DSF

The Heresy of Friar Travolo is now up at Daily Science Fiction.

This story combines medieval theological disputations and hyperbolic geometry. I’m quite proud of it.

#### The Cross-ratio

The **cross-ratio** of four points is .

By taking we define the cross-ratio on (ordered) quadruples of points on the real line, and thereby, by interpreting the differences as signed distances, on ordered quadruples of collinear points in Euclidean space. 311 more words