Spring 2013, TuTh, Science Center 216
My name: Andrew Cotton-Clay (please call me Andy)
Office: Science Center 527
Office Hours: M 12:30-1:30 and Th 2-3 or by appointment.
E-mail: acotton at math
Syllabus: Math 130 Syllabus
Course iSite: Math 130 iSite
Euclid's Elements: as pdf and as html
John Stillwell, The Four Pillars of Geometry: go to lib.harvard.edu and search e-resources for springerlink, then enter your Harvard login and search SpringerLink for the title.
1: due Sep 17
2: due Sep 24
3: due Oct 1
Midterm 1 corrections: due Oct 8
4: due Oct 15
5: due Oct 29
Sep 3: Introduction and brief discussion of Euclidean, Elliptic, and
Hyperbolic geometries. Discussion of Euclid's Elements, the postulates,
Propositions I.1-9 and hidden assumptions. Beginning of discussion of the
parallel postulate; see Euclid I.16,22,23,27.
Sep 5: Equivalence of Euclid's fifth postulate and Playfair's axiom (P),
with existence in P coming from hidden ``betweenness'' assumptions (which
fail on the sphere) and uniqueness coming from Euclid's fifth postulate
(which fails in the hyperbolic plane). See Euclid I.16,22,23,27. Axioms
for affine planes. Example of the smallest (four element) affine plane.
[Omitted summaries]
Oct 8: Three reflections theorem for spherical geometry, distance on S^2,
and the spherical law of cosines. See Ryan, Chapter 4.
Oct 10: Area of a spherical triangle is its angle excess (see Stillwell,
pages 190-191). O(3) as the isometry group of S^2, and a proof that every
element is a composition of reflections (see Ryan, Chapter 4).