Talk:Menger sponge

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You have new messages (last change).

This math block:

M_{n+1} := \left\{(x,y,z)\in\mathbb{R}: \exists i,j,k\in\{0,1,2\}: ((3x-i,3y-j,3z-k)\in M_n)\mbox{ and at most one of }i,j,k\mbox{ is equal to 1}\right\}

is too wide to fit on mid to small size screens (1024px or smaller). Could someone familiar with the notation find a good way to break it into two or more lines?

[edit] Incorrect?

I was editing the page Cantor dust, (adding a image of the 3D version of the set). There I found, the text talks about a 3D version of the Cantor dust and names it "the Menger sponge". But this page shows a 3D Sierpinski carpet. The images to the right shows the difference. Does anybody what's correct? // Solkoll 22:59, 29 Dec 2004 (UTC)

Both are correct, just different generalizations of the Cantor set in three dimensions. Both the Cantor dust and Menger sponge have the Cantor set within them, but also space around the Cantor set that is not directly described by the set. This space around the set is described by extending the set into multidimensions, but there are multiple ways to interpret the pattern of the Cantor set, as it does not directly define its construction in more dimensions. Pengwy 02:33, 22 May 2006 (UTC)

[edit] Sponge?=

It might be good to explain why this is a "sponge" and not a cube or something else.

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