definition -- payoff(s) / challenge(s) / game(s) / math(s) / plan(s)

* _ .. -- @ media / idea(s) / change(s) / theme(s) ? [:/] _

Möbius transformation

is a bijection on the extended complex plane \mathbb{C} \cup \{\infty\} given by
f(z) = \begin{cases} \frac{a}{c} &\text{if } z = \infty \\ \infty &\text{if } z = -{d \over c}\\ \frac{az+b}{cz+d} &\text{otherwise} \end{cases}
where a,b,c,d \in \mathbb{C} and ad - bc \ne 0

Riemann sphere / resource(s)

* - play / social(s) / machine(s) / method(s) / cycle(s) # ! @ Æ