Holditch's Theorem and results due to A. Broman are revisited and extended under geometric hypotheses. In addition, smoothness and convexity properties of Holditch curves are derived, with emphasis on the necessity of smoothness hypotheses on the parent curve.

Contact details are reproduced from the original publication and may be historical.

Harald Proppe

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

hal.proppe@concordia.ca

Alina Stancu

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

alina.stancu@concordia.ca

Ron J. Stern

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

stern@concordia.ca
  1. T. M. Apostol, M. A. Mnatsakanian: Subtangents – an aid to visual calculus, Amer. Math. Monthly 109 (2002) 525–533.https://doi.org/10.1080/00029890.2002.11919882Google Scholar
  2. A. Broman: Holditch’s theorem. A fresh look at a long-forgotten theorem, Math. Mag. 54(3) (1981) 99–108.https://doi.org/10.1080/0025570X.1981.11976908Google Scholar
  3. A. Broman: Holditch’s theorem is somewhat deeper than Holditch thought in 1858, Normat 3 (1979) 89–100 (in Swedish).Google Scholar
  4. F. H. Clarke, Yu. Ledyaev, R. Stern, P. Wolenski: Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics 178, Springer, New York (1998).Google Scholar
  5. H. Holditch: Geometrical theorem, Quart. J. 2 (1858) p. 38.Google Scholar

H. Proppe, A. Stancu, R. J. Stern. “On Holditch's Theorem and Holditch Curves.” Journal of Convex Analysis 24 (2017), No. 1, 239–259. https://doi.org/10.68381/jca24017