What is the significance of the mirror numbers?

Question

I'd like to hear insights and theory of the mirror numbers and their possible significance in mathematics and geometry. With mirror numbers I mean these four examples:

432 -> 234
123 -> 321
153 -> 351
987 -> 789

Sum of 432 & 234 is 666 and sum of 153 & 351 is 504, which are famous numbers from historical perspective, namely from Pythagoras, Plato, Archimedes and Revelation of John.

Supplementing questions arose on a chat with Dan:

1) How to determine if a number x can be represented as n + rev(n)?

2) How to determine possible n & rev(n) for number x?

Answer 1

This is not terrifically profound, but if $y$ is the mirror of $x$ in base $b$, then $x \equiv y \mod b-1$, while $x \equiv \sigma y \mod b+1$ where $\sigma = 1$ if $x$ and $y$ have an odd number of base-$b$ digits and $-1$ if they have an even number of base-$b$ digits.

Answer 2

Such pairs of numbers have no intrinsic mathematical significance (although related numbers are studied; see palindromic numbers) due to the arbitrary choice of base $10$. I don't know of any geometric connection but I would expect it to be very subtle, not as direct as what you are suggesting. The fact that there is both a 2-3-4 triangle and a 6-6-6 triangle is a coincidence emboldened by the choice of a relatively large base.