University of Connecticut

Events Calendar

Math Club
Hilbert's 3rd Problem
Michael Biro (UConn)

Wednesday, September 18, 2019
5:45pm – 6:35pm

Storrs Campus
Monteith 226

Polygons that can be cut up into congruent polygonal pieces are called equidecomposable. Two equidecomposable polygons have the same area, and it turns out the other direction is true too: two polygons with the same area are equidecomposable. This lets us describe what "equal area'' means for polygons without using calculus.

Hilbert asked if a similar result is true for polyhedra (the 3D-analogue of polygons, like a cube): is equal volume the same as being decomposable into congruent polyhedra? The answer is no, and this is due to Hilbert's PhD student Max Dehn.

In this talk we'll prove equal area = equidecomposable for polygons and see why the same approach doesn't work in 3 dimensions using a clever numerical invariant found by Dehn, now called the Dehn invariant.

Note: Free pizza and drinks!


Keith Conrad

Math Club (primary), UConn Master Calendar

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