Math 130, Fall 2015
Information for students
 Syllabus
 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 M. Hutchings.
 Policy on absences for tests and midterms.
 How to get an A in this class
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 (link) (if that link doesn't work, 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 (link)
Weekbyweek list of readings and activities
(will be updated throughout the course) Sept. 27th: A review of Hartshorne's Geometry: Euclid and Beyond Euclid by D. Henderson.
Week 2: Euclid's constructions with straightedge and compass.
 Stillwell, chapter 1 (and a little of chapter 2).
 Activity: Euclid: the game
 online version of Euclid's elements, with comments. You were given the definitions and postulates as a handout.
Week 3: Parallels, and the theory of area
 Stillwell, chapter 2
 Short reading: Commentary on Euclid's method of superposition, from Hartshorne. (despite the weird page numbering, these pages are in order!)
 111 ways to prove the pythagorean theorem
 Handout: Proposition 35 and 38 from the online version of Euclid's elements
 Euclid's construction of the regular pentagon, from Hartshorne. Compare with your construction from HW2.
 Constructible ngons, followed by a quick introduction to field extensions. From a wonderful book "Conjecture and Proof" by M. Laczkovich.
 (Optional) videos of Prof. Eisenbud and Gauss' 17gon: video 1 video 2
 (Optional) Viete's construction of the 7gon
 Reading from Hartshorne: sections 68
Week 6: Hilbert's axioms, continued.
 Reading from Hartshorne: sections 810
Week 7: Midterm exam on Tuesday, Intorduction to projective geometry on Thursday. Discussion of independent project.
 Reading to be done by the beginning of Week 8:
How to win the lottery with projective geometry
an excerpt from ``How not to be wrong" by Jordan Ellenberg. 
Midterm solutions
Midterm problem statements (with point values)
Week 8: Projective geometry
 Selection from Ellenberg, see above
 Reading from Stillwell, chapter 5.
 Just for fun: anamorphic drawing.
And a very sophisticated understanding of projective transformations in OK GO's music video The writing's on the wall.
Week 9: More projective geometry
 Selections from Stillwell, chapter 6
Week 10: Transformation groups, plane and spherical geometry.
 Stillwell, chapter 7

Quaternions and rotations
More than you wanted to know, but you might be especially interested in the practical advantages of using quaternions over ordinary matrices.
Week 11: Introduction to hyperbolic geometry
 More on quaternions and 4dimensional geometry: Hypernom the game. Explained here
 Stillwell, chapter 8 up to 8.4
 Mobius transformations: video by Douglas Arnold and Jonathan Rogness,
with explanation here
And an interactive applet by Terry Tao.
Weeks 1213: More hyperbolic geometry; practice for presentations
 Reading from Stillwell, chapter 8.
 Many tilings of hyperbolic space by Jos Leys
 movies of isometries of hyperbolic space by GoodmanStrauss
 Here is a template that you can use to make this Escher tessellation on a wrinklypaper model of hyperbolic space!
 Notes on area of hyperbolic triangles from the end of the last class.
Week 1415: Student presentations on independent projects.
Week ∞ (not part of the course, but on the horizon).
Some geometry books that you might like to read in the future
 The shape of space by J. Weeks. A wonderful introduction to geometry and topology and the question "what is the geometry of our universe?" There is a short (and less mathematical) movie inspired by the book here .
 ThreeDimensional Geometry and Topology by W. Thurston. This book begins with an introduction to the hyperbolic plane, and then goes much further...
Homework
Weekly homework assignments will be posted here. Problem set 1 due Tuesday, September 8
selected solutions  Problem set 2 due Tuesday, September 15
selected solutions  Problem set 3 due Tuesday, September 22
selected solutions
See above for links to the readings.
 and... Just for fun (not to hand in) challenge problem on equidecomposability. Due never, but tell me if you solve part b!
 Problem set 4 due Tuesday, September 29
selected solutions  No homework due Tuesday, October 6 (you have a midterm!)
 Problem set 5 due Tuesday, October 13
selected solutions  Independent project assignment
Some suggestions for topics  Problem set 6 due Tuesday, October 20
selected solutions  Problem set 7 due Tuesday, October 27
selected solutions  Problem set 8 due Tuesday, November 3
selected solutions  Problem set 9 due Tuesday, November 10
selected solutions  Problem set 10 due Tuesday, November 24.
Note: there was a typo in Question 3.c), which has now been corrected.
The formula given there is a special case of the GaussBonnet theorem which says that angle defect (in our case, 2pi  exerior angle sum) is equal to the area of a polygon multiplied by the curvature of the space.
Hyperbolic space has constant negative curvature, in our calculaions we're using curvature 1.
triangle paper
selected solutions to HW 10  Resources for your independent project:
General advice on how to get started writing
Guidlines for peer review of a paper
Grading rubric for oral presentation and written report  Presentation schedule
 Review for the final exam
Your final exam takes place on Wed, December 16, 3pm6pm, in the usual classroom. I will hold office hours on Monday and Tuesday, times to be announced by email.
(also here are the videos mentioned in the problem set: video 1 video 2
Note: the last problem should say "where k and n are relatively prime". This has been added to the statement!
Worksheets
Worksheets that were given in class Worksheet 1 from September 3
 Worksheet 2 from September 17
 Worksheet 3 from September 29
 Worksheet on anamorphic (perspective based) writing from October 13
 Worksheet 4 (Pappus theorem) from October 22
 Worksheet 5 (Rotations) from October 29
 Worksheet 6 (Tiling the plane with reflections) from November 12