Radius of Curvature of Catenary

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Consider the catenary (blue curve). Let
be an arbitrary point on the catenary and let
be the point where the normal to the catenary meets the
axis. Then the radius of curvature of the catenary at
is equal to the distance from
to
, that is,
, where
is the center of the osculating circle to the catenary at
.
Contributed by: Izidor Hafner (December 2012)
Open content licensed under CC BY-NC-SA
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Reference
[1] V. P. Minorsky, Problems in Higher Mathematics, Moscow: Mir Publishers, 1975, p. 217.
Permanent Citation
"Radius of Curvature of Catenary"
http://demonstrations.wolfram.com/RadiusOfCurvatureOfCatenary/
Wolfram Demonstrations Project
Published: December 13 2012