Math 130, Spring 2019

Information for students

bCourses Site
DSP students should speak to the instructor as soon as possible, even if you don't have a letter yet.
Guidelines on what to do if you think you may have a conflict between this class and your extracurricular activities. In particular, you must speak to the instructor before the end of the second week of classes.
Academic honesty in mathematics courses: A statement on cheating and plagiarism, courtesy of Michael Hutchings.
How to get an A in this class, courtesy of Kathryn Mann.


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 Reading: Stillwell 1.1 Handout: Euclid's Elements for the adventurous, here's a Greek version January 24: Euclid's constructions; Thales' theorem Reading: Stillwell 1.1–1.3 / Hartshorne 1–2 Random: story about Thales by Plutarch (starts at VI, goes onto page 419) Activity: Euclid: the game Activity: Play with Geogebra January 29: arithmetic with Euclidean constructions Reading: Stillwell 1.3–1.4 Review for Thursday: fields (16.1—2) Worksheet 1: click here * Homework 1: click here January 31: square roots; parallel postulate Reading: Stillwell 1.5–2.2 Reading: Critique of superposition, Hartshorne pp 31–34 February 5: area; Thales' theorem Reading: Stillwell 2.3–6 / Hartshorne 22 * Homework 2: click here February 7: equidecomposability Some resources: Hartshorne 22, Wikipedia, interactive demonstrations For fun: Hinged dissections February 12: constructibility Reading: field extensions Reading: Constructible n-gons and field extensions (from Conjecture and Proof by M. Laczkovich) Reading: Hartshorne 28–29 Video: Construction of 17-gon (other videos: 1 and 2) February 14: more constructibility; impossible constructions Reading: see February 12 * Homework 3: click here February 19: constructibility of regular polygons; Gauss–Wantzel theorem Reading: Regular polygons (from Galois Theory by Ian Stewart) February 21: Hilbert's axioms: incidence and betweenness Reading: Hartshorne 6–7 Notes on the real projective plane: click here * Homework 4: click here February 26: betweenness: plane/line separation; rays, angles, triangles Worksheet 2: click here Reading: Hartshorne 7 February 28: intro to project; more betweenness: crossbar theorem, "in between point" Reading: Hartshorne 7 March 5: Midterm (in class) Material: everything up to and including betweenness (Feb 26 class), all homework questions plane/line separation, angles, but no triangles, no crossbar theorem, no "in between point" You will be given a list of Hilbert's axioms You do not need to cite Euclid's axioms by number (you can assume unique lines); any construction will be "from the axioms" unless stated I will not ask you to reprove anything we did in class, but you might need to give definitions March 7: congruence axioms Reading: Hartshorne 8–9 * Homework 5: click here March 12: finishing Hilbert's axioms; starting projective geometry Reading: Hartshorne 10, Stillwell 5.1–5.3 Reading: How to Win the Lottery with Projective Geometry (from How Not To Be Wrong, by Jordan Ellenberg) March 14: projective geometry Reading: Stillwell 5.1–5.5 * Homework 6: click here March 19: fractional linear transformations; invariants Reading: Stillwell 5.5–5.9 March 21: cross-ratio; other projective planes Reading: Stillwell 5.7–5.9 April 2: projective Pappus, Desargues; planar ternary rings Reading: Stillwell 6 Worksheet 3: click here * Homework 7: click here April 4: geometry via transformation groups Reading: Stillwell 7.1–7.3 April 9: Möbius transformations; hyperbolic lines; angles Reading: Stillwell 8.1–8.5 * Homework 8: click here April 10: angles; disc model; hyperbolic distance Reading: Stillwell 8.6–8.7 April 16: area on sphere and hyperbolic plane Reading: Stillwell 8.5 April 18: practice presentations April 23, 35, 30, May 2: presentations May 16: Final exam (in class, 8:10am–11am) Details on bCourses announcement