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Parallel Curves

Published online by Cambridge University Press:  20 November 2018

G. P. Henderson
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In the Euclidean plane a curve C has a one-parameter family of parallel involutes and a unique evolute C* which coincides with the locus of the centres of the osculating circles of C. If is parallel to C, C* is also the evolute of . We will study parallel curves in n-dimensional Euclidean space and obtain generalizations of the properties given above.

We will study parallel curves in n-dimensional Euclidean space and obtain generalizations of the properties given above.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954, pp. 99 - 107
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Da Cunha, P. J., Du parallelisme dans l'espace Euclidien, Portugaliae Math., 2 (1941), 181–246.Google Scholar
2. Ince, E. L., Ordinary differentialI equations (London, 1927).Google Scholar