a^2 + b^2 (1)
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c^2
Law of cosines, replace C in terms of A and B and Theta...
c^2 = a^2 + b^2 - 2ab cos(theta) (2)
theta = 0; cos -> 1 (so subst with 1 early, reorder) theta = 180; cos-> -1
c^2 = a^2 - 2ab + b^2 (3)
c^2 = a^2 + 2ab + b^2` (3n)
c^2 = (a-b)^2 (4)
c^2 = (a+b)^2 (4n)
add dual number.
c^2 = ( (a-b)+e)^2 ) (5)
c^2 = ( (a+b)-e)^2 ) (5n)
c^2 = (a-b)^2 +2(a-b)e + 0 (6)
c^2 = (a+b)^2 -2(a+b)e + 0 (6n)
reduce top part....
a^2 + b^2 = (a+b)(a-b) (7)
Reassemble
(a+b)(a-b) / (a-b)^2 + 2(a-b)e (8) ( 7/6 )
(a+b)(a-b) / (a+b)^2 - 2(a+b)e (8n) ( 7/6n )
(a+b)(a-b) / (a-b)^2 + 2(a+b)e (8n - normalize, use 8)
remove (a+b) from 8n
if the other path is taken, it's infinite... (a+b)/(a-b) approaches infinity at A=B > 0
(a-b) / (a+b) + 2e (9n)
this is a plot of (a-b) / (a+b) + (2*0) and (b-a) / (a+b) + (2*0)
https://www.desmos.com/calculator/by1chyufxa
And near 0 x, * small b, M approaches inifnity... or is < 0. at large A and B it's 1. at small C it's infinity (unless you look at it as c = a+b - e or c = a-b + e (or b-a)