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Economical triangle-square dissection

✍ Scribed by M. J. Cohn

Publisher: Springer
Year: 1975
Tongue: English
Weight: 745 KB
Volume: 3
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00181377

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✦ Synopsis

In the 1830's, it was proved almost simultaneously by W. Bolyai and Gerwien that given any two polygons of equal area, it is possible to dissect one into a finite number of pieces which may be rearranged to form the other. In this paper the dissection of a triangle to give a square is considered. No estimate has been made previously on the economy of such a dissection. A dissection which is probably close in economy to the most economical dissection is found, and an estimate is made as to how uneconomical any dissection must be.

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