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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 1

Deforming the Nephroid into the Cayley Sextic and Beyond

Francisco Javier González Vieli0000-0002-2245-5757
Sayfa
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Yayın Tarihi
2026-04-22
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

When $d=0$ this curve is a nephroid, when $d=3r/2$ it is a Cayley sextic.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In $\mathbb{R}^2$, let $\Gamma$ be a fixed circle with centre $C$ and radius $r$, and $\ell$ a straight line at distance $d$ of $C$.
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Temel Bulgular & Veri:We study the curve which is the envelope of the circles whose centre lies on $\Gamma$ and which are tangent to $\ell$.
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Sonuç & Katkı:When $d=0$ this curve is a nephroid, when $d=3r/2$ it is a Cayley sextic.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Envelope · circles · tangent line

Abstract

In $\mathbb{R}^2$, let $\Gamma$ be a fixed circle with centre $C$ and radius $r$, and $\ell$ a straight line at distance $d$ of $C$. We study the curve which is the envelope of the circles whose centre lies on $\Gamma$ and which are tangent to $\ell$. When $d=0$ this curve is a nephroid, when $d=3r/2$ it is a Cayley sextic.

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Bu Makaleye Atıf Yap

Vieli, F. J. G. (2026). Deforming the Nephroid into the Cayley Sextic and Beyond. International Electronic Journal of Geometry, Volume: 19 Issue: 1. https://doi.org/10.36890/iejg.1793372

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Kaynakça (9)

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  8. Umehara, M., Saji, K., Yamada, K.: Differential geometry of curves and surfaces with singularities. World Scientific, New Jersey (2022).
  9. Wang, Y., Nishimura, T.: Envelopes created by circles families in the plane J. Geom. 115 (7) (2024). https://doi.org/10.1007/s00022-023-00708-z