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Hypercube (and further diminsions)
November 14, 2015 at 12:43 pm
(This post was last modified: November 14, 2015 at 12:44 pm by Combanitorics.)
Lately I've concluded that the only dimension higher than the third that I really understand is the fourth. It appears to me that since there can be a general solution to fourth order equations, that hypercubes must exist, since it's possible to describe one perfectly with algebra, and since such an algebraic description is always possible with the fourth order formula.
I'm still working on the further generalization of the cube to n dimensions. Does anyone have an idea how to visualize that, or know of a really good link?
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RE: Hypercube (and further diminsions)
November 14, 2015 at 1:09 pm
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RE: Hypercube (and further diminsions)
November 14, 2015 at 1:30 pm
(November 14, 2015 at 1:09 pm)zebo-the-fat Wrote: http://i.imgur.com/Lq8Xr.gif
That was good!
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RE: Hypercube (and further diminsions)
November 14, 2015 at 1:34 pm
I can only work with the mathematics, higher order dimensions are then very simple. Imagining what it would "look like" becomes nearly impossible for me at just 4 dimensions.
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RE: Hypercube (and further diminsions)
November 14, 2015 at 1:48 pm
(This post was last modified: November 14, 2015 at 1:48 pm by Alex K.)
Higher order polynomials also have solutions, I don't understand what you think is special about four in that respect...
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RE: Hypercube (and further diminsions)
November 14, 2015 at 2:00 pm
(November 14, 2015 at 1:48 pm)Quantum Wrote: Higher order polynomials also have solutions, I don't understand what you think is special about four in that respect...
Well it is more then a little mind bending when you try to imagine what it may look like.
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RE: Hypercube (and further diminsions)
November 14, 2015 at 3:03 pm
(This post was last modified: November 14, 2015 at 3:10 pm by Cyberman.)
You might like to try this 4D Rubik Cube:
http://superliminal.com/cube/cube.htm
I can do the boring old 3D one, but this gives me a headache.
(There's also a link to a 5D version, for those who consider sanity to be something that only applies to other people.)
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RE: Hypercube (and further diminsions)
December 4, 2015 at 10:04 pm
MIT is working on 4d printing and thats really interesting.
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RE: Hypercube (and further diminsions)
December 4, 2015 at 10:11 pm
(This post was last modified: December 4, 2015 at 10:12 pm by Reforged.)
Well. I've found my next research project.
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RE: Hypercube (and further diminsions)
December 4, 2015 at 11:40 pm
(This post was last modified: December 4, 2015 at 11:41 pm by vorlon13.)
(IANMTU)
A piece of string is essentially one dimensional (length) and in our three (physical) dimensional world it can be manipulated in those extra dimensions without damage.
So to, a sheet of paper is 2 dimensional (length and width) but can be manipulated in the third dimension without damage, like being rolled up and unrolled for instance.
It turns out a 3 dimensional object (such as your body) if it was placed into a 4 (physical) dimensional 'universe', it could be manipulated in that 4th physical dimension in surprising ways, WITHOUT damage.
Yes, starting at your anus (what is it with so many of my posts winding up there??) you could be turned inside out, and then turned back again the way you were, without breaking any bones, without killing you, and without any pain. This topic was breached in Star Trek, curiously, and a (IIRC) Klingon battle cruiser had its crew 'inverted', but unfortunately, the effect was not reversed. They didn't show it, just made reference to the crews 'shameful' condition, presumably before they were euth'd by their fellow, un-inverted Klingons.
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