EUDML

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 $A = (0, 0)$ , $B = (a + b, 0) \in E$ trace the curves $k_{A}, k_{B} \subset E^{'}$ 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 $F_{X} = \frac{[a F_{B} + b F_{A}]}{a + b} - π ν a b .$ In this paper, under the 1-parameter closed planar homothetic motion...

A generalization of the Holditch theorem for the planar homothetic motions

Salim Yüce; Nuri Kuruoğlu — 2005

Applications of Mathematics

In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.

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The Steiner formulas for the open planar homothetic motions.

On the polar moment of inertia of the projection curve.

The polar moment of inertia of the projection curve.

Computation of polar moments of inertia with Holditch type theorem.

The Holditch sickles for the open homothetic motions.

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

A generalization of the Holditch theorem for the planar homothetic motions