The generalized Holditch theorem for the homothetic motions on the planar kinematics

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Kuruoglu N., Yuce S.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.54, no.2, pp.337-340, 2004 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2004
  • Doi Number: 10.1023/b:cmaj.0000042372.51882.a6
  • Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.337-340
  • Keywords: Holditch theorem, homothetic motion, Steiner formula
  • Ondokuz Mayıs University Affiliated: No

Abstract

W. Blaschke and H. R. Muller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let E/E' be a I-parameter closed planar Euclidean motion with the rotation number v and the period T. Under the motion E/E', let two points A = (0, 0), B = (a + b, 0) is an element of E trace the curves k(A), k(B) subset of E' and let F-A, F-B be their orbit areas, respectively. If F-X is the orbit area of the orbit curve k of the point X = (a, 0) which is collinear with points A and B then