[McBeige]

I'm guessing it's irrational as in rational vs irrational numbers. Rational means a fraction of whole numbers, so irrational numbers are those which cannot be represented as such a fraction. A 1/4 turn is rational, a 1/pi turn is irrational.

I feel like the light has to be parallel for it to work, so sunlight is a better example than a table lamp. Although I can't imagine any rotation of a simple 3D lattice having a nonrepeating shadow. Perhaps a more complex 3D crystal is necessary?

[mcswell]

Rational/ irrational here depends on the unit of measurement. A full circle (360 degrees) is rational if you measure it in degrees, but irrational if you measure it in radians (it's 2 pi radians).

[anamexis]

By that logic, couldn't any number be deemed rational by just declaring it as a unit?