Henry Goodman wrote:

"baskitcaise" <baskitcaise@hotmail.com> wrote in message
news:2huff2Fh6uduU1@uni-berlin.de...

Henry Goodman adjusted his tin foil beanie and asbestos underwear to
write:

Um, Pi is transcendental. That means it never finishes or repeats.

Not quite. See below.

Has that been proven yet?

Yes. I think in the 18th century. (Hardy's "Pure Mathematics " says
that pi was proved to be transcendental by Lambert in1761)

No; that was Ferdinand Lindemann, in 1882. Johann Lambert's proof was
of the *irrationality* of pi -- but you're right to mention his
result in this context because it indeed established that pi "never
finishes or repeats". The transcendental numbers are a subset of the
irrationals; what distinguishes them is that they are not roots of
any algebraic equation. The square root of 2 is an example of an
irrational number that is *not* transcendental; while its decimal
representation never repeats, it *can* be (easily) constructed with a
compass and straight-edge. OTOH 'squaring the circle' is impossible
because pi is transcendental.

See <http://mathworld.wolfram.com/Pi.html> and

<http://mathworld.wolfram.com/TranscendentalNumber.html>.

-- 
Odysseus 17# @ 38Y