I was playing around with a question involving resistances in parallel. I realized that $n$ equal resistors (resistance $R$) in parallel have combined resistance $R/n$. I proved this using (mathematical) induction. Then I considered two resistors with ratio $1:2$ in parallel, e.g. a $3\Omega$ and $6\Omega$ resistor in parallel. Since $3=6/2$, we can view the $3\Omega$ resistor as two 6 ohm resistors in parallel. So the problem boils down to finding the resistance of three $6\Omega$ resistors in parallel, which is $6/3=2$.
So this law can be used to make resistances easy to calculate. Above we just easily calculated the combined resistance of a $3\Omega$ and $6\Omega$ resistor in parallel. Yes, we could also have done $(3*6)/(3+6)$, but I think what I did is much easier.
Question: Is this algorithm known/is there a general version of it?