Math 130, Spring 2019

Data has been removed until after Spring 2020

Information for students


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 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; Gauss–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, 8:10am–11am)