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Menger sponge

Posted on: December 29th, 2013 by
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This is not a puzzle, rather an interesting concept.
A Menger sponge is defined as follows:
1. Take a 1x1x1 cube and divide it into 27 smaller cubes like a Rubix cubes.
2. Remove the small cubes in the middle of each face, and the small cube in the center. We are left with 20 cubes.
3. Repeat steps 1,2 for each smaller cube.
4. Keep repeating this process infinitely. After doing this process n times, we have 20^n cubes. After doing this infinite times, we have what is called the Menger sponge.
Menger sponge

This sponge has infinite surface area and zero volume. It's one-dimensional analogue is the cantor set. It is an immeasurable object.

See this Wikipedia article for more details


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