# It's a bit hazy

Calculus Level 5

What is the probability an Eisenstein integer is visible from the origin (that is, a line from the origin to the integer does not intersect any other Eisenstein integers)?

Note: An Eisenstein integer is a complex number of the form $$a+b\omega$$ where $$\displaystyle \omega = \frac{-1+i\sqrt{3}}{2}$$ and $$a,b \in \mathbb{Z}$$. For example, $$1, \omega$$ and $$3+2\omega$$ are all Eisenstein integers.

×