- In geometry, a
catenoid is a type of surface,
arising by
rotating a
catenary curve about an axis (a
surface of revolution). It is a
minimal surface, meaning...
-
sense of
differential geometry. The
helicoid and the
catenoid are
parts of a
family of helicoid-
catenoid minimal surfaces. The
helicoid is
shaped like Archimedes...
-
cartographic projection necessarily distorts at
least some distances. The
catenoid and the
helicoid are two very different-looking surfaces. Nevertheless...
- of the catenary, and the
minimal surface of
revolution will thus be a
catenoid.
Solutions based on
discontinuous functions may also be defined. In particular...
- in the
design of
certain types of
arches and as a
cross section of the
catenoid—the
shape ****umed by a soap film
bounded by two
parallel circular rings...
-
defined a
sequence of
capillary shapes known as (1)
nodoid with 'neck', (2)
catenoid, (3)
unduloid with 'neck', (4) cylinder, (5)
unduloid with 'haunch' (6)...
- no
sharp edge at the gluing. If done with care the
result will be the
catenoid C {\displaystyle {\mathcal {C}}}
pictured at right, or
something similar...
- thrice-punctured torus.
Until its discovery, the plane,
helicoid and the
catenoid were
believed to be the only
embedded minimal surfaces that
could be formed...
- negatively-curved surfaces,
including the pseudosphere, helicoid, and
catenoid,
investigate mathematical toys, and use
these crocheted models "to explore...
- In 1776 Jean
Baptiste Marie Meusnier discovered that the
helicoid and
catenoid satisfy the
equation and that the
differential expression corresponds to...
