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A Three-Dimensional Pipe-Joining Problem

Published online by Cambridge University Press:  03 November 2016

M. D. Fox
M. D. Fox*
Affiliation:
Royal Latin School, Buckingham
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Extract

The problem is to join two given straight pipes by a curved pipe made up of two circular arcs of equal radii. The case when the two given pipes are coplanar has been discussed by E. Kosko in the Gazette of May 1964, pp. 192-196. Purely geometrical constructions for this case have been provided by S. N. Collings in the Gazette of October 1965, p. 302, and by me in the Gazette of February 1966, pp. 37-39. (Unfortunately Mr. Collings’s construction does not always work. On his diagram one can put in the two straight pipes in four different ways. For two of these ways the construction gives valid solutions, but for the other two ways the joining curve has a discontinuity of sense.)

Type
Research Article
Information
The Mathematical Gazette , Volume 53 , Issue 384 , May 1969 , pp. 142 - 147
Copyright
Copyright © Mathematical Association 1969

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