Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-01T19:06:37.047Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallel Curves

Published online by Cambridge University Press:  20 November 2018

G. P. Henderson
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

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