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Monotony of the Osculating Circles of Arcs of Cyclic OrderThree

Published online by Cambridge University Press:  20 November 2018

N. D. Lane ,
K. D. Singh  and
P. Scherk
N. D. Lane
Affiliation:
McMaster University and University of Toronto
K. D. Singh
Affiliation:
McMaster University and University of Toronto
P. Scherk
Affiliation:
McMaster University and University of Toronto
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It is well-known in elementary calculus that if a differentiable functionhas a monotone increasing curvature, then its curvature is continuous andthe circles of curvature at distinct points have no points in common. Inparticular, two one-sided osculating circles at distinct points of an arc A3 of cyclic order three have no points in common; cf. [l],[2], [3]. The conformai proof given here that any two general osculatingcircles at distinct points of A3 are disjoint (Theorem 1), may beof interest. We also prove that all but a countable number of points of A3 are strongly conformally differentiable (Theorem 2).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 265 - 271
Copyright
Copyright © Canadian Mathematical Society 1964

References

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