[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?

[function_seven]

It just occurred to me that when they’re talking about a “rational angle” they might be talking about a slope that can be specified rationally.

If you have a repeating three-dimensional crystal lattice, and a ray of light that is following an irrational slope, then it is guaranteed to intersect one of the cell units or vertices in that lattice.

If it did not intersect any nodes, then you would be able to express that slope rationally just by counting the number of vertical nodes over the number of horizontal nodes!

I’m assuming an infinite lattice here. For finite ones an irrational slope could still “sneak through”