# Catenoid

On this page:

- Definition of the noun Catenoid
- Explanation
- Printed dictionaries and other books with definitions for Catenoid
- Online dictionaries and encyclopedias with entries for Catenoid
- Photo about Catenoid
- Video about Catenoid
- Scrabble value of C
_{3}A_{1}T_{1}E_{1}N_{1}O_{1}I_{1}D_{2} - Anagrams of CATENOID
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## Definition of the noun Catenoid

What does Catenoid mean as a name of something?

**noun** - plural: catenoids

- [
*geometry*] A three-dimensional surface formed by rotation of a catenary

## Explanation

**Catenoid**: A catenoid is a surface in 3-dimensional Euclidean space arising by rotating a catenary curve about its directrix. Not counting the plane, it is the first minimal surface to be discovered. It was found and proved to be minimal by Leonhard Euler in 1744. Early work on the subject was published also by Jean Baptiste Meusnier. There are only two minimal surfaces of revolution: the plane and the catenoid.

- also known as 懸鏈曲面

## Printed dictionaries and other books with definitions for Catenoid

Click on a title to look inside that book (if available):

### Analysis and Mathematical Physics (1987)

by H. Triebel

*The generated rotation
-symmetric minimal surface is called catenoid*. We shall not discuss here how a ...

### Mathematical Conversations (2012)

Selections from The Mathematical Intelligencer by Robin Wilson, Jeremy Gray

Topologically, the plane and the helicoid are both once-punctured spheres and
* the catenoid is a twicepunctured sphere*. To complete this historical survey it is
necessary to weave in one more thread: Osserman's work on the global
properties ...

### Differential Geometry: Manifolds, Curves, and Surfaces (2012)

Manifolds, Curves, and Surfaces by Marcel Berger, Bernard Gostiaux

* The catenoid is a minimal surface because of the property of the center of
curvature of the catenary that can be seen on figure 10*.6.6.6.3 (see 8.7.20). Since
this property characterizes the catenary among plane curves, we see that the ...

### Elementary Differential Geometry (2001)

by Andrew Pressley

* The
catenoid is a surface of revolution*. In fact, apart 9. Minimal Surfaces 207 8.5.

### e-Study Guide for: Geometric Measure Theory: A Beginners Guide by Frank Morgan, ISBN 9780123744449 (2012)

by Cram101 Textbook Reviews

* A catenoid is a threedimensional shape made by rotating a catenary curve
around the z axis*. Not counting the plane, it is the first minimal surface to be
discovered. It was found and proved to be minimal by Leonhard Euler in 1744.
Early work ...

### Total Mean Curvature and Submanifolds of Finite Type (2014)

by Bang-Yen Chen

Hence * the catenoid is a surface of revolution with proper pointwise 1-type ∆ν =
Gauss map of the first kind*. Example 10.5. Consider the right cone Ca
parametrized by φ(u, v) = ( v cosu, v sinu, av ) , a > 0. Then the Gauss map ν is
given by ν ...

### Multivariable Mathematics (2016)

Mathematics, Mathematics by CTI Reviews

* A Catenoid is a three-dimensional shape made by rotating a catene curve
around the x axis*. Not counting the plane, it is the first minim: surface to be
discovered. It was found and proved to be minimal by Leonhard Euler in 1744.
Early work on ...

### Encyclopedia of Analytical Surfaces (2015)

by Sergey Krivoshapko, V.N. Ivanov

**Catenoid** **A catenoid** is formed by the revolution of a
catenary ...

### Encyclopaedia of Mathematics (2012)

by Michiel Hazewinkel

a specific kind – a plane, **a catenoid**, etc.; for instance, if the spherical image of
a complete minimal surface contains no open set on the sphere, then such a
minimal surface is a plane. 3) The generalization of Bernstein's theorem to
minimal ...

### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

**catenoid** The surface formed by rotating the *catenary about the x- axis. Under
certain conditions, the surface of minimal area bounded by two coaxial rings is **a
catenoid**. Seeminimal surface. Cauchy, Augustin-Louis, Baron (1789–1857) ...

### The Concise Oxford Dictionary of Mathematics (2009)

by Christopher Clapham, James Nicholson, James R. Nicholson

**catenoid** The surface
generated by rotating a *catenary around its axis of symmetry. Cauchy, Augustin-
Louis (1789-1857) One of the most important mathematicians of the early ...

### The American Illustrated Medical Dictionary (1916)

**catenoid** ...

### The Facts on File Dictionary of Mathematics (2009)

by John Daintith, Richard Rennie

**catenoid** /kat-ĕ-
noid/ The curved surface formed by rotating a catenary about its axis of symmetry.

## Online dictionaries and encyclopedias with entries for Catenoid

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## Photo about Catenoid

**catenoid**

Photo credit: fdecomite

## Video about Catenoid

**Catenoid Meaning**

Video shows what catenoid means. A three-dimensional surface formed by rotation of a catenary. Catenoid Meaning. How to pronounce, definition audio ...

## Scrabble value of C_{3}A_{1}T_{1}E_{1}N_{1}O_{1}I_{1}D_{2}

The value of this 8-letter word is 11 points. It is included in the first and second editions of the Official Scrabble Players Dictionary.

## Anagrams of CATENOID

What do you get if you rearrange the letters?

See also the blanagrams of Catenoid!

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