# catenoid

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Related to catenoid: helicoid

## catenoid

[′kat·ən‚ȯid]
(mathematics)
The surface of revolution obtained by rotating a catenary about a horizontal axis.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The catenoid reticulated shell consumes 3.9% more steel and has 5.6% smaller deflection than the spherical reticulated shell.
Caption: Figure 3: Six kinds of traditional rigid structural systems: (a) Kiewitt triangular pyramidal spherical reticulated shell (KPS); (b) geodesic triangular pyramidal spherical reticulated shell (GPS); (c) Kiewitt triangular pyramidal catenoid reticulated shell (KPC); (d) Kiewitt spherical reticulated megastructure (KSM); (e) rib-circle spherical reticulated megastructure (RSM); (f) rib-circle-reinforced spherical reticulated megastructure (RRSM).
On the critical value of the axisymmetric membrane stress-state of a catenoid shell.
Example 2 (the catenoid of the 1st kind is shown in Figure 1).
Therefore, the surface of catenoid of the 1st kind is minimal.
Instead, it would have a catenoid end (an end that looks like half a catenoid) and then an infinite sequence of parallel plane ends.
Another example of a complete minimal surface, called the catenoid, looks like an infinitely extended hourglass.
A sphere with two puncture points can be deformed into the infinitely extended hourglass form of a catenoid.
If a [not equal to] 0 and [alpha] = 0, that is, [M.sub.q,T] is the generalized catenoid of the first or the third kind (), then (4.13) implies that the function g(t) can be expressed in terms of elliptic functions and g(t) is not a rational function of t.

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