Introduction to "Pointwise Qualitative Factorization of 2-forms into 1-forms over ℝ4, PDF format; 175K.

I just know Calculus III, or calculus-based physics. Does this paper have any use whatsoever to me?

Then you should know about the cross product ×, and know what to feed into a four-function calculator to compute it:

(a1, a2, a3)×(b1, b2, b3) = (a2b3-a3b2, a3b1-a1b3, a1b2-a2b1)

If you have memorized the formula in x-y-z coordinates, just change the subscripts from x,y,z to 1,2,3 to convert. The coordinate formulation should look very similar to the coefficients I defined in the fact, the second part rewrites (in the paper's notation) to

(c23, -c13, c12)

There's some "stratosphere math" that explains how things are defined so this works out. Rather than go into that here, just use the result:

We can rephrase the entire paper to talk about making inferences about coordinates a1..4, b1..4 from the coordinates of the four cross-products

(a1, a2, a3)×(b1, b2, b3) = (c23, -c13, c12)
(a1, a2, a4)×(b1, b2, b4) = (c24, -c14, c12)
(a1, a3, a4)×(b1, b3, b4) = (c34, -c14, c13)
(a2, a3, a4)×(b2, b3, b4) = (c34, -c24, c23) site map
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