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Mar
28
revised How is the binomial expansion of the vectors?
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Mar
27
comment How is the binomial expansion of the vectors?
thanks for an interesting idea.. But then I lose the geometry of the vectors instantaneously :(
Mar
27
comment How is the binomial expansion of the vectors?
Yes. This is what I ended up myself. But, as mentioned in my second paragraph, there are some nice geometric properties for binomial expansion which fits very well with the vector sums. But this seems to stop at n=2.
Mar
27
awarded  Editor
Mar
27
revised How is the binomial expansion of the vectors?
added 14 characters in body
Mar
27
comment How is the binomial expansion of the vectors?
"Vectors (in the usual sense of the word) don't have a commutative (or even associative) multiplication operation, so the expansion doesn't even make sense." This is what I ended up with my own expansions. But then I couldn't believe that the nice juicy buildup of the vector additions as I mentioned in the question would abruptly stop at n = 2. I thought there would be a logical expansion on this to higher dimensions.
Mar
27
awarded  Student
Mar
27
asked How is the binomial expansion of the vectors?
Jun
17
comment How big is infinity?
There is a whole book on this topic. "Infinity and the Mind: The Science and Philosophy of the Infinite" by Rudy Rucker. It explains all the different types of infinities in mathematics. Quite an intimidating read for the non-mathematicians, though.
Mar
20
awarded  Supporter
Feb
17
comment Find third 3d coordinate given two other coordinates
The point which I wanted add is : For the above solution to work the line joining the center of the green and blue sphere has to be parallel to the box. This is not specified explicitly in the question.