A generalization of the Holditch Theorem for the planar homothetic motions

Yüce, Salîm; Kuruoğlu, N.

doi:10.1007/s10492-005-0005-3

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…Tutar and Kuruoğlu obtained the Steiner area formula and Holditch theorem for the one-parameter planar homothetic motions in the Euclidean plane [26]. In addition, Kuruoğlu and Yüce generalized the area formulas for planar motions and gave the corresponding formulas for homothetic motions [27][28][29][30]. This study is the most general form of all study about Holditch theorems obtained so far.…”

Section: Introductionmentioning

confidence: 94%

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

Eri̇şi̇r

2021

Advances in Mathematical Physics

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In this study, the planar kinematics has been studied in a generalized complex plane which is a geometric representation of the generalized complex number system. Firstly, the planar kinematic formulas with one parameter for homothetic motions in the generalized complex plane have been mentioned briefly. Then, the Steiner area formula given areas of the trajectories drawn by the points taken in a generalized complex plane have been obtained during the one-parameter planar homothetic motion. Finally, the Holditch theorem, which gives the relationship between these areas of trajectories, has been expressed for homothetic motions in a generalized complex plane. So, this theorem obtained in this study is the most general form of all Holditch theorems obtained so far.

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Section: Introductionmentioning

confidence: 94%

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

Eri̇şi̇r

2021

Advances in Mathematical Physics

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“…Tutar and Kuruoǧlu obtained Steiner area formula and Holditch theorem for the one parameter planar homothetic motions 25 . In addition, Kuruoǧlu and Yüce generalized the area formulas for planar motions, and gave the corresponding formulas for homothetic motions 26,27,28,29 . This study is the most general form of all study about Holditch theorems obtained so far.…”

Section: Introductionmentioning

confidence: 99%

Generalized Holditch Theorem for Homothetic Motions in Cp

Erişir

2024

Preprint

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In this study, the planar kinematics is studied in generalized complex plane which is a geometric representation of the generalized complex number system. Firstly, the one parameter planar kinematic formulas for homothetic motions in the generalized complex plane mentioned briefly. Then, the Steiner area formula given areas of the trajectories drawn by the points taken in generalized complex plane are obtained during the one parameter planar homothetic motion. Finally, the Holditch theorem, which gives the relationship between these areas of trajectories, is expressed for homothetic motions in generalized complex plane. So, this theorem obtained in this study is the most general form of all Holditch theorems obtained so far.

show abstract

A generalization of the Holditch Theorem for the planar homothetic motions

Cited by 2 publications

References 6 publications

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

Generalized Holditch Theorem for Homothetic Motions in Cp

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A generalization of the Holditch Theorem for the planar homothetic motions

Cited by 2 publications

References 6 publications

A New Construction of Holditch Theorem for Homothetic Motions in C p

A New Construction of Holditch Theorem for Homothetic Motions in C p

Generalized Holditch Theorem for Homothetic Motions in Cp

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A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$