# Number Systems in 3D

Number Systems in 3D

The points are the set , which is the first approximation of the fractional part in the base- system with digits.

:∈{0,1,...,n-1}

-l

∑

i=-l

i

z

a

i

a

i

z

n

This is a natural generalization of ordinary numeration systems with complex bases, but this time we treat the space as , where the first coordinate is along and the second is in the plane orthogonal to . Addition and multiplication are done component-wise using the coordinates, and , .

u=(cosψ,sinψ,1)

u

1=(1,1)

z=(r,r)

φ