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Monotony of the Osculating Circles of Arcs of Cyclic Order Three
Published online by Cambridge University Press: 20 November 2018
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It is well-known in elementary calculus that if a differentiable function has a monotone increasing curvature, then its curvature is continuous and the circles of curvature at distinct points have no points in common. In particular, 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 osculating circles at distinct points of A3 are disjoint (Theorem 1), may be of interest. We also prove that all but a countable number of points of A3 are strongly conformally differentiable (Theorem 2).
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- Copyright © Canadian Mathematical Society 1964
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