Abstract / résuméCUMC / CCEM 2005

Name / nom: Alexander Duncan

School / école: University of Toronto

Length / durée: 50 min

Title / titre: Dissections of Rectangles into Squares

Abstract / résumé: A dissection of a rectangle is an arrangement of non-overlapping squares that constitute a rectangle. A long-standing problem was to find a "perfect squared square" -- a square who's constituent squares are all of different sizes. The problem was solved by a team of undergraduates in the 1930s by exploiting a surprising connection with the theory of electric circuits. A resistor network is a graph-theoretic abstraction modelled after Kirchoff's famous voltage and current laws. There is a near bijective correspondence between "squared rectangles" and certain resistor networks. This talk explores this correspondence and demonstrates how the first "perfect squared square" was found.

Prerequisites / choses nécessaires: No background knowledge is assumed.



PDF format / format PDF: duncan.pdf