In my geometry studies, I learned that one can get the angle between two vectors with this formula:
I.e., the cosine of the angle equals the dot product of the two vectors over the product of their magnitudes.
Here we get about 1.05 radians or about 60.26 degrees. A cool thing about this formula is it works for vectors of any (matching) dimension, i.e., 3-D coordinates, 4-D coordinates, etc.
This is definitely doable in Emacs Calc, since we have a dot product function, called inner-product (press ‘x inner product’), But doing the angle formula involves a lot of steps, with either stack rotation or storing the vectors in variables. So I wanted to get the angle formula stored as a calc formula. Unfortunately, inner-product itself is only an interactive function, so this was problematic. However, inner-product actual calls another function, inner. So, this formula is possible:
arccos(inner(mul, add, v1, v2) / (abs(v1) abs(v2)))
How do you store this formula in Emacs? I could walk you through the steps described in section 18.4 of the Emacs Calc info manual, but the end result is that this code is stored in your ~/.emacs.d/calc.el:
(put 'calc-define 'calc-vectorsangle '(progn (defun calc-vectorsangle nil (interactive) (calc-wrapper (calc-enter-result 2 "vect" (cons (quote calcFunc-vectorsangle) (calc-top-list-n 2))))) (put 'calc-vectorsangle 'calc-user-defn 't) (defun calcFunc-vectorsangle (v1 v2) (math-normalize (list (quote calcFunc-arccos) (list (quote /) (list (quote calcFunc-inner) (quote (var mul var-mul)) (quote (var add var-add)) v1 v2) (list (quote *) (list (quote calcFunc-abs) v1) (list (quote calcFunc-abs) v2)))))) (put 'calcFunc-vectorsangle 'calc-user-defn '(calcFunc-arccos (/ (calcFunc-inner (var mul var-mul) (var add var-add) (var v1 var-v1) (var v2 var-v2)) (* (calcFunc-abs (var v1 var-v1)) (calcFunc-abs (var v2 var-v2)))))) (define-key calc-mode-map "zA" 'calc-vectorsangle) ))
Then when you start calc, you can put two vectors on the stack, and enter command ‘x vectorsangle’ or ‘z A’ for short:
This will work for vectors with as many more coordinates as you want, so long as there are the same number in each vector.