Graduate/Faculty Seminar
Friday, September 10, 1999, 4:00pm, 120 Physics
Richard Hain (Duke University Department of Mathematics)
Scissors Congruence
Abstract:- If two polygons in the plane can be cut up into congruent pieces, they have the same area. It has been long known that the converse is also true. (This is a good exercise which will be solved in the talk.) Likewise, in three dimensions, two polyhedra have the same volume if they can be decomposed into congruent pieces. Is the converse true? This was one of the problems Hilbert posed at the end of the 19th century. Dehn gave a clever solution soon after Hilbert posed the problem which has lead to important connections with number theory and algebra. I'll explain what "scissors congruence" problems are and give a brief idea of their connections to algebra.
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