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Parallel Curves

  • 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.

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References

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