Difference between revisions of "Iso-optic curve"
From Encyclopedia of Mathematics
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| − | A plane curve that is the locus of a vertex of given angle | + | {{TEX|done}} |
| + | A plane curve that is the locus of a vertex of given angle $\gamma$ that moves in the plane in such a way that its sides are tangents to a given curve for all positions of the angle. If $\gamma=\pi/2$, then the iso-optic curve is called an ortho-optic curve. For example, the ortho-optic curve of an ellipse is a circle. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)</TD></TR | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)</TD></TR> |
| − | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> K. Fladt, "Analytische Geometrie spezieller Kurven" , Akad. Verlagsgesell. (1962)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Berger, "Geometry" , '''I''' , Springer (1987) pp. 232</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> M. Berger, "Geometry" , '''II''' , Springer (1987) pp. 239</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top"> F.G. Texeira, "Traité des courbes spéciales remarquables planes on gauches" , Coïmbre (1908–1915)</TD></TR></table> | |
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Latest revision as of 16:54, 8 April 2023
A plane curve that is the locus of a vertex of given angle $\gamma$ that moves in the plane in such a way that its sides are tangents to a given curve for all positions of the angle. If $\gamma=\pi/2$, then the iso-optic curve is called an ortho-optic curve. For example, the ortho-optic curve of an ellipse is a circle.
References
| [1] | A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) |
| [a1] | K. Fladt, "Analytische Geometrie spezieller Kurven" , Akad. Verlagsgesell. (1962) |
| [a2] | M. Berger, "Geometry" , I , Springer (1987) pp. 232 |
| [a3] | M. Berger, "Geometry" , II , Springer (1987) pp. 239 |
| [a4] | F.G. Texeira, "Traité des courbes spéciales remarquables planes on gauches" , Coïmbre (1908–1915) |
How to Cite This Entry:
Iso-optic curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Iso-optic_curve&oldid=15086
Iso-optic curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Iso-optic_curve&oldid=15086
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article