Higher-dimensional geometry by Technomancer
Inspired by The_Powder_Boy's 'Dimensions' save (id:1824768). Created using 12Me21's keyboard/signwriter. Be warned, this is a bit 'teacherish', and you will need at least a basic understanding of coordinate geometry to get anything out of it.
Comments
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juanchacon99 19th May 2017
It's easy to explain, the hard part is to actually create a 4D object... -
00yoshi 1st Oct 2015
Well, now we need to project a 4D thing into the 3D space to send rendering instructions to the GPU to project and draw them into 2D space... -
00yoshi 1st Oct 2015Well, you are really insane if you really used an ingame signwriter...
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JusticeFighter 1st Oct 2015
Great! Now make a new one explaining negative dimensions! >:D -
sentinal-5 7th Aug 2015
i like this :) it's a nice simple explanation of >3 dimentional coordinates that i'm sure most people will be able to grasp (and that's not something that is easy to write). i love it how you've managed to avoid all the "it just does okay"s of higher dimention education such as why the cubes that form the net of a classical tesseract all contact eachother without being deformed. +1 for a great description -
Normal321 15th Jul 2015
It's quite a good explanation, I ussualy try to visualise a tesseract in the form of "3 dimensional cube grid" if you know what i mean. In this situation it would made up of 8 cubes. Anyway, good save and +1 -
Technomancer 15th Jul 2015
*stack, not grid (sorry for the triple post) -
Technomancer 15th Jul 2015And the reason why there are 10 cubes per row/rows per sheet/sheets per grid is purely because I had already stated that each cube was 10 units on a side, and a cube (or Nth-order hypercube) is by definition equal in all dimensions (ie, all axes are the same length).
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Technomancer 15th Jul 2015Indeed they do not. I just picked cubes for 'demonstration purposes' because their geometry is simple and easy to visualize. If it helps, the cube actually represents an arbitrary volume of hyperspace (!) surrounding your preferred brand of higher-dimensional object . The object itself is of unspecified form and is what I identified as P (I referred to it as a point, but this is meant to denote its location rather than its form)
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Normal321 15th Jul 2015Excuse me but shouldn't there be 8 cubes in one tesseract? Also higher dimensional objects doesn't necesarily need to be cubes ro "cubelike".