Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20090518 01:40:41
Three dimension mathsOne could say the real number line is one dimensional. Then, one could say that imaginary numbers give us a second dimension, and complex numbers allow us to 'explore' the plane. So, what piece of maths allows us to 'move' into a threedimensional space? #2 20090518 04:04:21
Re: Three dimension mathsThere's no similar way to pull a third dimension from the complex numbers, because the complex numbers are algebraically closed. Why did the vector cross the road? It wanted to be normal. #3 20090518 04:26:59
Re: Three dimension maths
It is important to keep in mind that this is one way to look at the complex numbers, but not the only way. The complex numbers form a 2 dimensional vector space over the real numbers, with multiplication defined in a funny way. They actually have a lot more properties than that, but this is just one view. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20090518 04:54:11
Re: Three dimension mathsThank you both. The words "algebraically closed" tell me what I needed to know, but I hadn't made the leap that rules out 3D. when I have some time to spare I think I had better look Quaternions up in Wiki and hope I can understand some of that. Last edited by random_fruit (20090518 05:05:48) 