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Difference between revisions of "Iso-optic curve"

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A plane curve that is the locus of a vertex of given angle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052710/i0527101.png" /> 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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052710/i0527102.png" />, then the iso-optic curve is called an ortho-optic curve. For example, the ortho-optic curve of an ellipse is a circle.
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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====

Revision as of 11:54, 5 July 2014

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)


Comments

References

[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=32377
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article