The plane transcendental curve describing the form of a homogeneous flexible string of fixed length and with fixed ends attained under the action of gravity (see Fig.).
In Cartesian coordinates its equation is
The length of an arc beginning at the point is
The radius of curvature is
The area bounded by an arc of the catenary, two of its ordinates and the -axis is
If an arc of a catenary is rotated around the -axis, it forms a catenoid.
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
|[a1]||J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)|
Catenary. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Catenary&oldid=16508