h a l f b a k e r yMake mine a double.
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Tetrahedron. Cube. Octahedron. Dodecahedron. Icosahedron. Bor-ing!
Let's not limit ourselves to the so-called laws of mathematics. Or at the very least expand the definition as to include (and name) some of the more interesting "perfect solids" such as the Dove bath bar and the overstuffed recliner.
Toiletron
http://www.halfbakery.com/idea/Toiletron
"Conratulations! A perfect solid" [hippo, Jun 25 2001, last modified Oct 05 2004]
Platonic Solids
http://www.littleex...th/geometry/solids/
[The Military, Jun 25 2001, last modified Oct 21 2004]
(?) Dragon Fractal
http://www.usd431.n...ragon%20fractal.gif
Not as it appears. [nineteenthly, Dec 17 2008]
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Or perfect semisolids: <insert names of favorite star or starlet here> |
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I nominate the Lego-brickagon... |
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Would this lead to new dice for Dungeons and Dragons? |
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[centauri] No no no no no: |
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DM: Role a dice to see wether you hit |
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DM: the D176.23213 of course, you know.. the one thats shaped like a boing 747 crossed with an elephant... |
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hmm.. cant see that catching on... |
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Left alignment indicates a new annotation? I thought they just left aligned when there was enough room below the links. |
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[centauri]: Left alignment appears to begin first paragraph below links, new annotation or not, pursuant to a suggestion yesterday. |
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See link to Platonic Solids. The doughnut (torus), in all its innate perfection, just falls short. |
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Perfect solids? basic solids? platonic solids? |
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Whatever names you use, these are the only solids from which deviation (variation) can occur, in our space now and for ever more. Search for "Coxeter-regular-polytopes. |
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If architecture etc is boring when using the basic solids its not because the solids are boring but because the variation in the forms geometry has not been explored, perhaps designers don't know how to produce forms using technical drawing. |
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Is that what, contributer "The Military" was ruminating on? Desarges, French Mathematician, was intially prevented from spreading technical drawing science for military reasons! |
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Didn't the North beat the South aided by manufacturing weapons using technical drawing to introduce parts that were interchangeable. I do have reference for this. |
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And [uked] wins this year's Vernon Prize for completely meaningless and incomprehensible theorising on the halfbakery. And it's only Jan 6th! I guess that means I don't need to read any more of this site till next year. |
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Too soon to give that prize out 'stu...Besides, this is just todays episode of "What the Hell was That?" |
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pottedstu: thanks, at last aclaim. time to come clean, I am a teacher. If you, or any one else wants to argue, then all you have to do is 1: use a dictionary, that's what words mean ( check the date of publication 1st) Coxeter is the ultimate reference in three and more than three dimensions. I understand three-dimensIonal structures (Hood) the rest is beyond me. I am not a mathematician, I am an artist, because of my engineering background I have been employed to teach technical drawing. |
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There are a limited number of solids, in this and any any universe, anywhere in this and any universe. Please argue. Point =1, inside and outside (sphere)=2, flat=3, (points) tetrahedron (pyramid) =4 (points). Five, that's your homework. |
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PS I am not a maths teacher - they're all asleep? |
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....and who do you run to when you want the toner changed in the photocopier? |
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[Robert] For some reason the idea of a Boing 747 has made me smile for at least 30 minutes now and may well be adopted into Shropshire parlance. Jolly well done. |
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Memphis-style pork-barbeque sandwich-now THERE'S a perfect solid!!! |
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But wouldn't you need some equations in there?... |
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Here're two (rushed) parametric equations for a crown (these are curves but if you look at them as bounded by the x-y plane they look like crowns): |
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They both take the form C(t) = p(cos t)(1,0,0) + p(sin t)(0,1,0) + z(t)(0,0,1) |
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In the realistic looking one where it's actually got points: z(t) = h cos (t mod (2pi/n))... (but n >= 2 for it to work properly) |
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In the nice one where I've got curves for points: z(t) = h|sin(n(t mod (n*pi))/2)|... (this one works with all values of n) |
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p is it's radius, h is it's height, and n is the number of points on your crown... |
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DISCLAIMER: These are rushed, I've only seen them drawn in my head, |
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In high school, I made a 60-sided polyhedron out of right triangles. It was nothing but folded paper... no tape or anything like that. It took three hours. -- kevin the NERD |
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That's nothing. I made a perfect sphere out of a year's worth of nail clippings and hair grease. |
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Then they cleaned the cell out and threw the ball away :( |
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//a 60-sided polyhedron out of right triangles// I'm imagining that would be a bit like an icosahedron where each of the original twenty triangular faces was then built out into a small pyramid. Is that on the right track? |
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//but can we keep the dodecahedrons?
I like 'em//
Maybe they'll go the way of the dododecahedrons. |
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//Would this lead to new dice for Dungeons and Dragons?// |
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I'm still looking forward to the introduction of the D7. |
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Since dra- is the Greek prefix used to denote acting (i.e. dra-ma,) - a "dra-gon" must be some kind of two-dimensional polygonal shape that somehow manages to pretend to be something else. |
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Maybe the Dragon Fractal, whose true shape can never be perceived? [link] |
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