Math 128, Modern Geometry

D. Joyce, Clark University

3 Oct 2005

Due Friday. From Chapter 6: 3abc, 6, 7ab, 10.

Read Chapter 7. We’ll discuss it next time.

Last time. Families of Steiner circles of the first and second kinds. Elliptic, hyperbolic, and loxadromic transformations. Transformations with one fixed point. Degenerate families of Steiner circles.

Today. Return test. Discuss any ideas about what we’re working on for the Pythagorean theorem. Quick review of the topics last time. Preview of hyperbolic geometry including a bit of history and how we’re going to approach it from Möbius geometry. Look at the hyperbolic tilings at

   http://www.aleph0.edu/∼djoyce/poincare/poincare.html