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Level: BSc, MSci, MSc
Title: Rigid frameworks
Supervisor:

Prof. Bill Jackson
Research Area: Combinatorics
Description:

A bar-and-joint framework is a straight line realization of a graph in d-dimensional Euclidean space. We think of the framework as a collection of bars and joints where vertices correspond to joints and each edge to a bar joining its end-vertices. The framework is rigid if it has no non-trivial continuous deformations. Thus a triangle in the plane is rigid but a square is not since it can be continuously deformed into a parallelogram. The project is to give a survey of results on the rigidity of frameworks.
Further Reading:
  • J. E. Graver, Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures. Dolciani Mathematical Expositions number 25, Mathematical Association of America, 2001 (ISBN: 0-88385-331-0).
Key Modules:
Other Information:

Knowledge of Graph Theory and Linear Algebra is a prerequisite.
Current Availability: Yes