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File:Torus from rectangle.gif

Torus_from_rectangle.gif (400 × 300 pixels, file size: 262 KB, MIME type: image/gif, looped, 49 frames, 14 s)

Description

A torus can be constructed by two transformations on a rectangle. First, we bend along one direction, joining opposite sides, creating a cylinder. Then, we bend the cylinder so the ends are joined. The resulting figure is a torus. However, the second transformation does not preserve lengths on the surface, as can be observed by the extension and compression of the checkered pattern.

Here's the diagram of this process:

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Author Lucas Vieira
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Captions

Converting the floor board to torus with three steps. Checkerboard > Cylinder > Torus.

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URL: https://commons.wikimedia.org/wiki/user:LucasVB
author name string: Lucas Vieira
Wikimedia username: LucasVB

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Date/TimeThumbnailDimensionsUserComment
current10:30, 22 May 2012Thumbnail for version as of 10:30, 22 May 2012400 × 300 (262 KB)LucasVB{{Information |Description=A torus can be constructed by two transformations on a rectangle. First, we bend along one direction, joining opposite sides, in order to create a cylinder. Then, we bend the cylinder so the ends are joined. The resulting fig...

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Quelle: https://en.wikipedia.org/wiki/File:Torus_from_rectangle.gif