Geodesic
Monotony of the Osculating Circles of Arcs of Cyclic OrderThree
Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 265-271

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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). 
Lane, N. D.; Singh, K. D.; Scherk, P. Monotony of the Osculating Circles of Arcs of Cyclic OrderThree. Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 265-271. doi: 10.4153/CMB-1964-024-0
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     title = {Monotony of the {Osculating} {Circles} of {Arcs} of {Cyclic} {OrderThree}},
     journal = {Canadian mathematical bulletin},
     pages = {265--271},
     year = {1964},
     volume = {7},
     number = {2},
     doi = {10.4153/CMB-1964-024-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1964-024-0/}
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