All sorts of phrases and words have a different meaning in science than they do in the general public. Some scientists argue that the misunderstood terms should simply be replaced, but that just prolongs the problem. If "theory" is replaced with some other word, then it's almost inevitable that word will also be misused every now and again. Instead, a better science education is in order to teach the majority of the population to understand the terms scientists use to define our reality. So, without further adieu...
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This picture illustrates the vertices and edges of a 5-dimensional hypercube, also known as a penteract. It has 32 vertices, 80 edges, 80 two-dimensional faces, 40 three-dimensional faces and 10 four-dimensional faces.
Hypercubes are examples of regular polytopes. These are multidimensional analogues of the familiar Platonic solids in three dimensions, namely the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron. In dimensions five and higher, there exist analogues of the tetrahedron, of the cube (pictured), and of the octahedron, but there are no other regular polytopes. In dimension four, things are more interesting: there exist analogues of the dodecahedron and icosahedron, as well as the 24-cell, which has no analogue in any other dimension. I wrote a detailed post about this in March 2013, which you can find here: https://plus.google.com/101584889282878921052/posts/HJxUtVJ16zn
The illustration is an excerpt from a very nice video by Oliver Knill (polytopes.mov). The video illustrates all of the regular polytopes in four and five dimensions by using successive stereographic projections. If you like polytopes, this video is well worth seven minutes of your time.
This beautiful animated Gif, created by Reuben Thomas (http://www.functor.co/), is circulating on G+ without significant information about what it is.
Let's see what it is.
It's Menger sponge, a particular 3D fractal, described for the first time in 1926 by Karl Menger, while he was exploring the concept of topological dimension. Menger sponge is the three-dimensional extension of the Cantor set and Sierpinski carpet.
The Menger sponge simultaneously exhibits an infinite surface area and encloses zero volume.
How it is constructed
According to Wikipedia, the construction of a Menger sponge can be described as follows:
1. Begin with a cube.
2. Divide every face of the cube into 9 squares, like a Rubik's Cube. This will sub-divide the cube into 27 smaller cubes.
3. Remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a Void Cube).
4. Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration will give you a level-2 sponge, the third iteration gives a level-3 sponge, and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.
Read here for knowing more:
Watch an interactive Menger sponge: http://www.mathematik.com/Menger/Menger2.html
Menger Sponge Animations: http://www.pure-mirage.com/html/Optimized%20Menger%20Sponges.htm
A level-3 Menger sponge built by students at Mississippi State University out of 48,000 folded business cards:
Video: Trip inside a 3D fractal (Menger Sponge level 14)
Trip inside a 3D fractal (Menger Sponge level 14)
Read also the interesting post of :
#menger_sponge #fractal #fractal_geometry #mathematics
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