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

Nuri KuruoğluSalim Yüce — 2004

Czechoslovak Mathematical Journal

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 = [ a F B + b F A ] a + b - π ν a b . In this paper, under the 1-parameter closed planar homothetic motion...

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