Center of curvature
(Redirected from Center of Curvature)
In geometry, the center of curvature of a curve is a point located at a distance from the curve
curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve.[1] The locus of centers of curvature for each point on the curve comprise the evolute of the curve. This term is generally used in physics regarding the study of lenses and mirrors (see radius of curvature (optics)).
It can also be defined as the spherical distance between the point at which all the rays falling on a lens or mirror either seems to converge to (in the case of convex lenses and concave mirrors) or diverge from (in the case of concave lenses or convex mirrors) and the lens or mirror itself. It lies on the principal axis of a mirror. In case of a convex mirror it lies behind the polished surface and it lies in front of the reflecting surface in case of a concave mirror.[2]
See also
[edit]References
[edit]- ^ *Borovik, Alexandre; Katz, Mikhail G. (2011), "Who gave you the Cauchy--Weierstrass tale? The dual history of rigorous calculus", Foundations of Science, 17 (3): 245–276, arXiv:1108.2885, doi:10.1007/s10699-011-9235-x, S2CID 119320059
- ^ Trinklein, Frederick E. (1992). Modern physics (7th ed.). Austin: Holt, Rinehart and Winston. ISBN 0-03-074317-6. OCLC 25702491.
Bibliography
[edit]- Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), New York: Chelsea, ISBN 978-0-8284-0087-9
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