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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2021 / Cilt: 37 - Sayı: 1

Homothetic Motions and Dual Transformations

Homotetik Hareketler ve Dual Dönüşümler

Yusuf YAYLI
Gülsüm YÜCA
Pages
194–205
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we study on homothetic motions in dual spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this research, we produce a homothetic motion in 𝐸1𝑛 from a homothetic motion in 𝐸𝑛 by using a dual transformation.
📊
Key Findings & Data:Then, we examine the invariance of the axis of the umbrella motion that is 𝑥⃗=(1,1,..,1) in both spaces.
💡
Conclusion & Impact:Finally, we study on homothetic motions in dual spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this research, we produce a homothetic motion in 𝐸1𝑛 from a homothetic motion in 𝐸𝑛 by using a dual transformation. Furthermore, we define a transition from Euclidean umbrella matrix to Lorentzian umbrella matrix. Then, we examine the invariance of the axis of the umbrella motion that is 𝑥⃗=(1,1,..,1) in both spaces. We also provide examples to make our results clear. Moreover, we draw their figures to investigate visual representations. Finally, we study on homothetic motions in dual spaces.

Özet

Bu çalışmada, dual dönüşüm yardımıyla 𝐸1𝑛 deki homotetik hareketlerden 𝐸𝑛 de homotetik hareketler elde ettik. Ayrıca, Öklidyen şemsiye matrisleri ile Lorentzian şemsiye matrisleri arasında bir geçiş sağladık. Daha sonra, şemsiye hareketinin ekseni olan 𝑥⃗=(1,1,..,1) in iki uzayda da sabit kaldığını gösterdik. Elde edilen sonuçların pekiştirilmesi amacıyla örnekler vererek şekillerini çizdik. Son olarak, homotetik hareketleri dual uzaylarda çalıştık.

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Cite This Article

YAYLI, Y., YÜCA, G. (2022). Homothetic Motions and Dual Transformations. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 37 - Sayı: 1, 194–205. https://ajindex.com/articles/503221

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