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