# A Meditation on π

**note:** This is *not* a volley in the \(\pi-\tau\) debate, of which Vi Hart is undisputed monarch -- and right, as well -- as far as I'm concerned.

### (1)

A few number-theoretic \(\pi\) facts:

- \(\pi\) is provably transcendental, thus also irrational.
- \(\pi\) is suspected, but not known, to be normal, a generalization of transcendence.
- \(\pi\), provably, has Liouville-Roth constant (or
*irrationality coefficient*) no greater than \(7.6063\), and is suspected to have constant no greater than \(2.5\). (As a consequence of its irrationality, its L-R constant is \(\geq2\).)

Note, though, that each of these things is also true of *literally 100% of numbers*. And before you scoff at my use of the figurative 'literally', no no -- measure-theoretically, the non-(normal, transcendental, irrational, irrationality-coefficient-less-than-8) numbers make up exactly, mathematically 0% of the number line.

For the record: irrational algebraics like \(\sqrt2\) are *also* nonterminating and nonrepeating, and it's not clear what features of the stringwise-local decimal expansion (which seems to be the only thing \(\pi\) enthusiasts focus on,