O'Meara Mathematics Libraries > Mini Menger Sponge

Menger Sponge

Menger's sponge (sometimes wrongly called Sierpinski's Sponge) is a fractal solid that can be described as follows. Take a cube, divide it into 27 = 3 x 3 x 3 smaller cubes of the same size and remove the cube in the center and the six cubes that share faces with it. You are left with the eight small corner cubes and twelve small edge cubes holding them together. Now, imagine repeating this process on each of the remaining 20 cubes. Repeat again. And again ...

Menger's Sponge is named for its inventor, Austrian mathematician Karl Menger (1902-1985). For more information about fractals and Menger's Sponge, visit the following web site:

Self Similar Fractals
Fractals - Fractal Dimension

or look for "The Fractal Geometry of Nature" by B. Mandelbrot (W.H.Freeman 1982) in your local bookstore or library.


So.. come to the O'Meara Mathematics Library and say hello to "Mini"!  She is a mini-Menger sponge in other words, a mathematical object made into art.  She is also a featured part of our exhibit on Dr. Karl Menger, a mathematics professor at Notre Dame from 1937 to 1946.  

She was constructed by the Mathematics Club of Cornell College, Iowa, http://orgs.cornellcollege.edu/mathclub/ and http://orgs.cornellcollege.edu/mathclub/sponge/sponge.mov.  She was brought to Notre Dame by Dr. Jim Freeman, professor of mathematics, an alum of Notre Dame.

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