# Math 130, Spring 2019

## Data has been removed until after Spring 2020

### Information for students

### Textbook

The required text for this course is *The Four Pillars of Geometry* by John Stillwell. You can download a copy of this book for free on campus through the UC library (if that link doesn't work, just search for the book at lib.berkeley.edu). This book is a wonderful introduction, but a little *too easy* for us, so there will be *lots* of required supplementary readings supplied by the instructor. We will also use some excerpts from Hartshorne's *Geometry: Euclid and Beyond
Euclid*. I recommend this to students wishing to go further. It can also be downloaded on campus.
### Homework, Readings, etc.

(will be updated throughout the course)

**January 22:** intro, Euclid's postulates
**January 24:** Euclid's constructions; Thales' theorem
**January 29:** arithmetic with Euclidean constructions
**January 31:** square roots; parallel postulate
**February 5:** area; Thales' theorem
**February 7:** equidecomposability
**February 12:** constructibility
**February 14:** more constructibility; impossible constructions
**February 19:** constructibility of regular polygons; Gaussâ€“Wantzel theorem
**February 21:** Hilbert's axioms: incidence and betweenness
**February 26:** betweenness: plane/line separation; rays, angles, triangles
**February 28:** intro to project; more betweenness: crossbar theorem, "in between point"
**March 5**: Midterm (in class)
**March 7:** congruence axioms
**March 12:** finishing Hilbert's axioms; starting projective geometry
**March 14:** projective geometry
**March 19:** fractional linear transformations; invariants
**March 21:** cross-ratio; other projective planes
**April 2:** projective Pappus, Desargues; planar ternary rings
**April 4:** geometry via transformation groups
**April 9:** Möbius transformations; hyperbolic lines; angles
**April 10:** angles; disc model; hyperbolic distance
**April 16:** area on sphere and hyperbolic plane
**April 18:** practice presentations
**April 23, 35, 30, May 2:** presentations
**May 16:** Final exam (in class, 8:10amâ€“11am)

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