Revolution of the Catenary
Revolution of the Catenary is a surface of revolution, given by a parametrisation, immersed.
Open Revolution of the Catenary in the interactive viewer →
aperiodic def-parametric immersed implemented revolution tradition-classical
Formula
Properties
- Family
- revolution
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
- Exactness
- elementary
Definition
the catenary z = a cosh(rho/a) revolved about its axis of symmetry; a = 1 and base radius 1.6 fixed to the operator defaults
Sources
Chart reproduced numerically against the shipped implementation: fwd max 0.28 of tol, 0.0% of oracle beyond tol (tol floor 2.5 x 0.02217).
- Revolution of the catenary (alysseid), z = a cosh(rho/a) about the catenary's axis of symmetry -- the catenoid's companion, and not minimal: R. Ferreol, ibid., chapter "alysseide".
- Revolution of the sinusoid, x = a cos(z/b) about Oz -- a string of onion-dome beads meeting in cusp circles on the axis: R. Ferreol, ibid., chapter "surface de revolution de la sinusoide" (the chapter dates its study to 2012).
- D. von Seggern, "CRC Standard Curves and Surfaces" (1993), p. 304 -- Fresnel's elasticity surface.
- A. Robin (2004), plotted after M. Trott, "The Mathematica GuideBook for Graphics" (2004), p. 103 -- the paper bag surface.
- O. Knill (2017); M. A. Villarino and J. C. Varilly (2024) -- the trihyperboloid and its volume ln 256.
- C. Dupin, "Applications de Geometrie et de Mechanique", Paris 1822;
- R. Ferreol, "Revolution of the catenary (Alysseid)", Encyclopedie des formes mathematiques remarquables, mathcurve.com; local mirror chapter ch1366_alysseid_2 (S:/data/math_art/references/websites/mathcurve/book/surfaces/ch1366_alysseid_2.md).