The Ribbon of Moebius by claude19

3D Modeling • Abstract • posted on Feb 06, 2009

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Description

XenoDream without postwork Frame and text with PhotoFiltre En topologie, le ruban de Möbius (aussi appelé bande de Möbius ou anneau de Möbius) est une surface fermée dont le bord se réduit à un cercle. Elle a la particularité d'être réglée et non-orientable. Cette surface a été décrite indépendamment en 1858 par les mathématiciens August Ferdinand Möbius (1790-1868) et Johann Benedict Listing (1808-1882). Le nom du premier fut retenu grâce à un mémoire présenté à l'Académie des sciences à Paris. On trouve également les dénominations de bande, anneau ou ceinture de Möbius ou, abusivement et phonétiquement, de Moebius, notamment dans les traductions. Il est facile de visualiser la bande de Möbius dans l'espace : un modèle simple se réalise en faisant subir une torsion d'un demi-tour à une longue bande de papier, puis en collant les deux extrémités. Si l'on coupe le ruban en deux dans le sens de la longueur, on obtient un anneau unique, vrillé, mais qui possède deux faces distinctes et deux bords distincts. Si on le recoupe dans le sens de la longueur, on obtient... deux anneaux distincts, vrillés et entortillés l'un sur l'autre. The Möbius strip or Möbius band (alternatively written Mobius or Moebius in English) is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It is also a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858. A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. In Euclidean space there are in fact two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. The Möbius strip is therefore chiral, which is to say that it has "handedness" (as in right-handed or left-handed).

Comments (23)

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3x3

12:42AM | Fri, 06 February 2009

interesting concept my friend!

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koosievantutte

12:53AM | Fri, 06 February 2009

very fine and clever modeling!

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MagikUnicorn

1:11AM | Fri, 06 February 2009

Sublime design...Ont ce la gele ici Oufff

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fractalbeke

2:24AM | Fri, 06 February 2009

Je dois dire qu'ici reigne un sentiment d'épatamment et ce pour la raison suivante : Votre volontée d'aler à la découverte/reconnaissance des chemins sinueux de XD et ce avec un progrès certain.

M2A

2:42AM | Fri, 06 February 2009

A great mathematical illustration from the August Ferdinand Möbius work. Sobriety and strength are well featured. (in Academy, "Moebius" instead of Möbius is considered as a mistake naming:)

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pops

3:13AM | Fri, 06 February 2009

You've done it again exceptional image

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carlx

3:55AM | Fri, 06 February 2009

Excellent image and design, Claude!!!

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adrie

3:59AM | Fri, 06 February 2009

Wow awesome design and colours....excellent done.

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A_Sunbeam

5:51AM | Fri, 06 February 2009

Nicely done!

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lyron

6:30AM | Fri, 06 February 2009

Wonderful design!!

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LivingPixels

7:19AM | Fri, 06 February 2009

Class Claude very classy and beautiful image!!!

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MrsRatbag

8:27AM | Fri, 06 February 2009

Very very cool image!

watchman2005

1:31PM | Fri, 06 February 2009

A nice take on an old theme, nice one!!!!

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kleinhoon

2:19PM | Fri, 06 February 2009

Beautiful design!

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Richardphotos

2:52PM | Fri, 06 February 2009

superb XD Claude

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lizzibell

7:31PM | Fri, 06 February 2009

Beautiful design...

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three_grrr

7:40PM | Fri, 06 February 2009

Another wonderful XD form, and a very informative narrative as well. You are learning XD very well!

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amota99517

3:28AM | Sat, 07 February 2009

Outstanding!!!! You are doing such great things in this program.

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jocko500

9:44AM | Sat, 07 February 2009

real cool design

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mtc

11:01AM | Sat, 07 February 2009

Pour moi, c'est notamment un très beau mouvement, et qui nous invite à la musique par quelque chose d'une bien jolie (presque) clé de sol. Congrats, Claude!

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