The Heilbronn Triangle Problem: History and Recent Developments


Title: The Heilbronn Triangle Problem: History and Recent Developments

Speaker: Eion Mulrenin

Date/Time/Location: Friday. September 2nd, at 2:00pm, NES 102

Abstract: The Heilbronn triangle problem is an old problem in discrete geometry which seeks to maximize the value of the smallest area of the triangles formed between triples of any set of n points in the unit square. More precisely, for a configuration $D_n$ of $n$ points in $[0,1]^2$, set $\Delta(D_n)$ to be the smallest area of a triangle formed between any three points of $D_n$. The Heilbronn problem then asks for the value of $\Delta(n) := \sup \Delta(D_n)$, where the supremum is taken over all configurations $D_n$. We wish to present an overview of the interesting history of this problem, discuss some recent developments and results, and pose several related open problems and variants.

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