Automated exploration of inner isoptics of an ellipse
| العنوان: | Automated exploration of inner isoptics of an ellipse |
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| المؤلفون: | Thierry Dana-Picard, Witold Mozgawa |
| المصدر: | Journal of Geometry. 111 |
| بيانات النشر: | Springer Science and Business Media LLC, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | 010102 general mathematics, 0211 other engineering and technologies, Regular polygon, Tangent, 02 engineering and technology, Ellipse, 01 natural sciences, Combinatorics, Conic section, Point (geometry), Geometry and Topology, 0101 mathematics, Orthoptic, 021101 geological & geomatics engineering, Mathematics |
| الوصف: | For a given curve $${\mathcal {C}}$$ and a given angle $$\theta $$ , the $$\theta $$ -isoptic curve of $${\mathcal {C}}$$ is the geometric locus of points through which passes a pair of tangents to $${\mathcal {C}}$$ making an angle equal to $$\theta $$ . If the curve $${\mathcal {C}}$$ is smooth and convex, isoptics exist for any angle, and through every point exterior to the curve, there is exactly one pair of tangents. The isoptics of conics are well known. In this paper, we explore the inner isoptics of ellipses, i.e. the envelopes of the lines joining the points of contact of the ellipse with the tangents through points on a given isoptic. If $$\theta =90^{\circ }$$ , the isoptic is called orthoptic and the corresponding inner isoptic is called the inner orthoptic. We show that the inner orthoptic of an ellipse is an ellipse, but in general the inner isoptics are more complicated. |
| تدمد: | 1420-8997 0047-2468 |
| DOI: | 10.1007/s00022-020-00546-3 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::370ebeff424dec291c952b9ea7390aa5 https://doi.org/10.1007/s00022-020-00546-3 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi...........370ebeff424dec291c952b9ea7390aa5 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 14208997 00472468 |
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| DOI: | 10.1007/s00022-020-00546-3 |