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Czechoslovak Mathematical Journal, vol.54, no.2, pp.337-340, 2004 (SCI-Expanded)
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].