Totally awesome: Dimensions:
Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed!
Hat-tip: quixote
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I love the 4th dimension. I plan on spending the rest of my life in it. I've published a number of things about it, and am deep into researching others. I've taught it to teenagers and grad students. There are some wonderful Youtube videos with animations for seeing 4th dimension polytopes. My 4th grade science fair first prize for "The Fourth Dimension" was implemented in Tinker Toys.
But two comments: first, why stop at four? Second, one needs to distinguish flat Euclidean space with hyperbolic space, most importantly Minkowski 4-dimensional space which is where the kingdom of Special Relativity reigns, within the Empire of General Relativity. Again, why stop at four? String theory is hyped, but still pretty. And there are weird and wonderful things in spaces of an infinite number of dimensions.
That was one of the best math videos I have ever seen. The fourth dimension was really cool, the mandelbrot set was especially beautiful, and I can't believe imaginary is so useful in geometry.
@jonathan
I love the 4th dimension too! I have been interested in it since 7th grade. They make for really cool shapes when they translate into the third dimension. I also felt sad that it was impossible to visualize the fourth dimension, since we are out of that realm. Oh, and what is that thing about infinite dimensions? That sounds really cool.
Jonathan Vos Post: You have the smarts, I have an animator geek who vastly enjoyed the dimension videos and needs new work for his portfolio. Why don't we get together and make some of those videos? Serious.