Sine and cosine represent the movements you need to draw a unit circle (with a two axis plotter). It is unfortunate if we don't introduce them like that.https://twitter.com/ThingsWork/status/1089272107119325185 …
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If you add links that connect points that are not adjacent in 2D, you create a 3rd dimension. If you don't overdo it, this will just be a curved 2D space. If you add more links over longer distances, the 2D space can fold into a full 3D space. It also works for going to 4D.
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If you only contract the distances in a 3D lattice a little bit, you get a curved 3 space (gravity), but if you go further, it folds up into more dimensions. Unfortunately, rotations in 4D are no longer commutative, in 8D no longer associative, and beyond there are no rotations.
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