scholarly journals The Generalized Holditch Theorem for the Homothetic Motions on the Planar Kinematics

2004 ◽  
Vol 54 (2) ◽  
pp. 337-340 ◽  
Author(s):  
N. Kuruoğlu ◽  
S. Yüce
Keyword(s):  
Holditch Theorem

scholarly journals A generalization of the Holditch Theorem for the planar homothetic motions

2005 ◽  
Vol 50 (2) ◽  
pp. 87-91
Author(s):  
Salim Yüce ◽  
Nuri Kuruoğlu
Keyword(s):  
Holditch Theorem

A New Generalization of the Steiner Formula and the Holditch Theorem

2015 ◽  
Vol 26 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Tülay Erişir ◽  
Mehmet Ali Güngör ◽  
Murat Tosun
Keyword(s):  
Holditch Theorem ◽  
Steiner Formula

The areas of the trajectory surface under the Galilean motions in the Galilean space

2018 ◽  
Vol 15 (09) ◽  
pp. 1850162 ◽  
Author(s):  
Mücahi̇t Akbiyik ◽  
Sali̇m Yüce
Keyword(s):  
Type Theorem ◽  
Holditch Theorem ◽  
Periodic Rotation ◽  
Galilean Space ◽  
Appl Math

In the literature, Holditch theorem was obtained under periodic rotation and translation motions in [H. Holditch, Geometrical theorem, Q. J. Pure Appl. Math. 2 (1858) 38] or periodic shear and translation motions in [O. Röschel, Der satz von Holditch in der isotropen ebene. Abh. Braunschweig. Wiss. Ges. 36 (1984) 27–32]. In this paper, by introducing the projection of a vector onto a plane, scalar area, area vector of a surface, we investigate Holditch theorem under periodic rotation, translation and shear motions. We give two interpretations for the Holditch type theorem in Galilean space.

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