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


KURUOĞLU N., YÜCE S.

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

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2004
  • Doi Number: 10.1023/b:cmaj.0000042372.51882.a6
  • Title of Journal : CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Page Numbers: pp.337-340

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