As a teenager - the concept of irrational numbers fascinated me. The idea that all possible numbers existed in PI.
From that I reasoned that any piece of data you have now also existed in PI somewhere. For a moment I thought that this could lead to a brilliant compression algorithm, where you could simply point to the index and range in PI where your particular piece of data existed. When I got older I realised that the index was likely to be larger than the piece of data you were storing, making it a bad compression trade-off.
Now I'm sure this line of thinking must fit into a branch of Mathematics somewhere - but I'm not sure where to look.
My question is: What is the term for 'PI-indexing'?
EDIT: A related example - here is an example of a filesystem that stores files as locations in PI.
First of all, it's only suspected that all numbers occur as substrings of the decimal expansion of $\pi$. Almost every number has this property, but it's actually incredibly difficult to show that the property holds for any one specific number, with the exception of certain numbers constructed for the sole purpose of having this property.
The general area of math here would be "irrational number theory."