Curvature of the Focal Conic in the Isotropic Plane
It is shown in \cite{beba} that every focal conic $\mathcal{C}$ in the isotropic plane can be represented by the equation $y^2=\epsilon x^2+x$, $\epsilon \in \{-1,0,1\}$ and a parametrization. This paper gives the equation of the circle of curvature at the point $T$ of the focal conic $\mathcal{C}$....
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| Published in | Sarajevo journal of mathematics Vol. 6; no. 1; pp. 117 - 123 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
11.06.2024
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| Online Access | Get full text |
| ISSN | 1840-0655 2233-1964 |
| DOI | 10.5644/SJM.06.1.10 |
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| Summary: | It is shown in \cite{beba} that every focal conic $\mathcal{C}$ in the isotropic plane can be represented by the equation $y^2=\epsilon x^2+x$, $\epsilon \in \{-1,0,1\}$ and a parametrization. This paper gives the equation of the circle of curvature at the point $T$ of the focal conic $\mathcal{C}$. The radius of curvature $\rho$ at the point $T$ of the focal conic $\mathcal{C}$ is given as well as its relation to the span $\delta $ from the center of $\mathcal{C}$ to the tangent $\lijepot$ at the point $T$ and to the length of the half diameter of $\mathcal{C}$ on the diameter parallel to the $\textup{tangent}$.
2000 Mathematics Subject Classification. 51N25 |
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| ISSN: | 1840-0655 2233-1964 |
| DOI: | 10.5644/SJM.06.1.10 |