Menger Sponge
 |
A Fractal which is the 3-D analog of the Sierpinski Carpet. Let 
be the numberof filled boxes, 
the length of a side of a hole, and 
the fractional Volume after the 
thiteration.
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
The Capacity Dimension is therefore
 | |  | |
|  | ||
|  | (4) |
J. Mosely is leading an effort to construct a large Menger sponge out of old business cards.
See also Sierpinski Carpet, Tetrix
References
Dickau, R. M. ``Menger (Sierpinski) Sponge.''http://forum.swarthmore.edu/advanced/robertd/sponge.html. Mosely, J. ``Menger's Sponge (Depth 3).'' http://world.std.com/~j9/sponge/.
- Subtend
- Subtraction
- Succeeds
- Successes
- Sufficient
- Suitable Number
- Sum
- Summand
- Summatory Function
- Sum-Product Number
- Sum Rule
- Sup
- Characteristic (Partial Differential Equation)
- Characteristic Polynomial
- Characteristic (Real Number)
- Character (Multiplicative)
- Character (Number Theory)
- Character Table
- Charlier's Check
- Chasles-Cayley-Brill Formula
- Chasles's Contact Theorem
- Chasles's Polars Theorem
- Chasles's Theorem
- Chebyshev Approximation Formula
- Chebyshev Constants