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

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KURUOĞLU N., YÜCE S.

Czechoslovak Mathematical Journal, cilt.54, sa.2, ss.337-340, 2004 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 2
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1023/b:cmaj.0000042372.51882.a6
  • Dergi Adı: Czechoslovak Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.337-340
  • Anahtar Kelimeler: Holditch Theorem, homothetic motion, Steiner formula
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

W. Blaschke and H. R. Müller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let E/E′ be a 1-parameter closed planar Euclidean motion with the rotation number ν and the period T. Under the motion E/E′, let two points A = (0, 0), B = (a + b, 0) ∈ E trace the curves k A , k B ⊂ 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 F X = [aF B + bF A ]/a+b -πνab. In this paper, under the 1-parameter closed planar homothetic motion with the homothetic scale h = h(t), the generalization given above by W. Blaschke and H. R. Müller is expressed and F X = [aF B + bF A ]/a+b - h 2 (t 0 ) πνab, is obtained, where ∃t 0 ∈ [0,T].