On the contrary, mathematics makes use of "modulo 2π" (that's "2 pi") somewhat often. In particular, in discussing Fourier series, you consider functions defined on the circle, which is often thought of as the reals R modulo 2π. Most of the suggested fraction modulus functions here do the right thing.

The "niceness" of integer moduli is that the following is true: (($a % $m) + ($b % $m)) % $m == ($a + $b) % $m and (($a % $m) * ($b % $m)) % $m == ($a * $b) % $m. However, even for non-integer moduli, the former is true.