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Journals / International Electronic Journal of Geometry / 2024 / Volume: 17 Issue: 2

Apollonius Problem and Caustics of an Ellipsoid

Yagub Aliyev(ADA Üniversitesi)0000-0003-1698-4297
Pages
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Publication Date
2024-10-27
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AI Summary & Key Takeaways

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

The main motivation of this paper is to classify all possible cases of these intersections.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the paper we discuss Apollonius Problem on the number of normals of an ellipse passing through a given point.
📊
Key Findings & Data:The problem is then generalized for 3 dimensional space, namely for Ellipsoids.
💡
Conclusion & Impact:The main motivation of this paper is to classify all possible cases of these intersections.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ellipsoid · Apollonius · centro-surface

Abstract

In the paper we discuss Apollonius Problem on the number of normals of an ellipse passing through a given point. It is known that the number is dependent on the position of the given point with respect to a certain astroida. The intersection points of the astroida and the ellipse are used to study the case when the given point is on the ellipse. The problem is then generalized for 3 dimensional space, namely for Ellipsoids. The number of concurrent normals in this case is known to be dependent on the position of the given point with respect to caustics of the ellipsoid. If the given point is on the ellipsoid then the number of normals is dependent on position of the point with respect to the intersections of the ellipsoid with its caustics. The main motivation of this paper is to classify all possible cases of these intersections.

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Cite This Article

Aliyev, Y. (2024). Apollonius Problem and Caustics of an Ellipsoid. International Electronic Journal of Geometry, Volume: 17 Issue: 2. https://doi.org/10.36890/iejg.1368456

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