You wrong. Perfect number is 1,884955781 ( or Pi / 5 * value in modulo )
For answer the question, first you need to know, that exactly Wave Texture node do.
So I build in simpler nodes exact copy of Wave Texture node:
This node setup produce similar result as Wave Texture node, and you can check this:
So now we can follow the nodes, to know where 1.8888 is hidden.
We begin in modulo coordinates here, from reference question. As i see, you have 3 repeats, so I think you set 0.3333 in modulo. You didn't give any information about it, but it's looks like that I'm right.
z now is from
Next stop is my node setup, in first nodes texture coordinates are multiplying with the result of this two:
First, multiply 10:
Next it is our X-number, that you think is 1.8888. I call him X, so result is
Last stop - sine. You need to know, that Sine repeats in 2*Pi period. So now we can get eaquation:
So X will be:
So, you wrong. perfect number is 1,884955781