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Discrete
and Combinatorial Geometry
- Mark Nielsen
Professor Nielsen's research interests include a wide range of topics in
discrete and combinatorial geometry. The appeal of these problems is their
intrinsic interest and lack of prerequisite machinery. For instance:
If T is any (non-equilateral) triangle and we assign each point of the
plane one of two colors, is it always possible to find three points of the
same color that form the vertex set of a triangle congruet to T?
If J is a simple closed curve in the plane, is it always possible
to find four points on J that form the vertices of a square?
Given a set S of n points in the plane, what types of
geometric behavior can be guaranteed to exist among the subsets of S?
None of these have complete answers to date, but all have interesting partial
results that raise interesting and approachable questions.
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