401 Seminar S06

Math 401
Spring 2007

Tuesday, Thursday in Malott 224

1:25 to 2:40 PM

Instructor: Bob Connelly (connelly@math.cornell.edu) Office hours: TBA

Schedule of talks

Date	Tuesday	Thursday
1/23-25/2007	Introduction	Mark, Fourier Analsis and Difraction
1/30-2/1/2007	Sara, Oragami Mathematics	Matthew, Simplex Method
2/6-8/2007	Keith, Protein Rigidity	Rami, Flexible Surfaces
2/13-15/2007	Steve, Bracing Grids	Bob, Reverse Isoperimetric Inequality and Packing
2/20-22/2007	Mark, Minkowski Geometry	Bob, Cauchy's Rigidity Theorem
2/27-3/1/2007	Matthew, Isoperimetric Inequality	Rami, Four Vertex Theorem
3/6-9/2007	Sara, Geometry and Billiards	Keith, Classical Greek Problems
3/13-15/2007	Steve, Morley's Theorem	Mark, Art Gallery Theorems
3/20-22/2007	SPRING BREAK	SPRING BREAK
3/27-29/2007	Matthew, Euler's formula	Rami, Archimedes Theorem
4/3-5/2007	Bob is out of town (Maria Terrell will sit in) Steve, the 17-gon	Bob is out of town (Maria Terrell will sit in) Sara, Geometry of SO(3)
4/10-12/2007	Matt, Chomp	Mark, Buffon's Needle Problem and Bertrand's Paradox
4/17-19/2007	Keith, Slopes for Point Configurations (extra)	Steve, Euler Line, proof 2
4/24-26/2007	Rami, Minimal Surfaces	Recap
5/1-3/2007	Sara, Hilbert's Third Problem	Keith, Planar Subsets of a Hypercube +

Possible Topics

My preference is for topics in discrete geoemetry, and the following are some initial suggestions. Students will almost all of the talking, and we all will be responsible for keeping the speaker honest and clear.

Cauchy's Theorem about the rigidity of polyhedra.
The construction of flexible triangulated surfaces.
Tracing polynomial curves with linkages in the plane.
The impossibility of trisecting an angle with ruler and compass constructions.
Curves of constant breadth and Fourier expansions of the radius of curvature.
Aperiodic tilings.
The most dense packing of congruent disks in the plane.
Dissecting polyhedra in the plane and space -- Hilbert's third problem.
Mathematical paper folding.
The stability of tensegrity structures.
Constructing hyperbolic geometry.
Helly's theorem about intersections of convex sets.
Gallai's theorem about points and lines in the plane.
The Beckmann-Quarles theorem about unit-distance preserving maps of the plane.

Part of the experience will be to learn how to gain access to the materials needed. The following are some books that are on reserve in the Mathematics library that can provide a starting point for deciding what to cover.

Proofs from the Book: Ziegler
Geometry and the Imagination: Hilbert and Cohn-Vossen
What is Mathematics?: Courant and Robbins
The Enjoyment of Mathematics: Rademacher and Toeplitz
Convex figures: Lyusternik
Combinatorial Geometry: Pach and Agarwal
Studies in Global Geometry and Analysis: ed. Chern
Old and New Unsolved Problems in Plane Geometry and Number Theory: Klee and Wagon

Another very useful tool is http://www.ams.org/mathscinet/ (not to mention Wikipedia) which is available on most Cornell terminals.

Stay tuned at this web page for updates and a schedule of who is talking.

Link to the Math Department.

Last updated: August 16, 2007