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# Catenoid

## Definition of the noun Catenoid

What does Catenoid mean as a name of something?

noun - plural: catenoids

1. [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

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### 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 ...

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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catenoid

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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 C3A1T1E1N1O1I1D2

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?