On the Dissection of Rectangles into Right-Angled Isosceles Triangles

Authors: Skinner J.D.¹; Smith C.A.B.²; Tutte W.T.³

Source: Journal of Combinatorial Theory, Series B, Volume 80, Number 2, November 2000 , pp. 277-319(43)

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Abstract:

We consider the problem of dissecting a rectangle or a square into unequal right-angled isosceles triangles. This is regarded as a generalization of the well-known and much-solved problem of dissecting such figures into unequal squares. There is an analogous “electrical” theory but it is based on digraphs instead of graphs and has an appropriate modification of Kirchhoff's first law. The operation of reversing all edges in the digraph is found to be of great help in the construction of “perfect” dissected squares. Copyright 2000 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: 1740 North 59th Street, Lincoln, Nebraska, 68505-1123 2: 141 Portland Crescent, Stanmore, HA7 1LR, England 3: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Publication date: 2000-11-01