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


KURUOĞLU N., YÜCE S.

CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.54, ss.337-340, 2004 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 54 Konu: 2
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1023/b:cmaj.0000042372.51882.a6
  • Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Sayfa Sayısı: ss.337-340

Özet

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