That pi is irrational was first proved by Johan Heinrich Lambert in 1761, and there are a whole bunch of other proofs for it since then. The final nail was placed by Lindemann who proved that pi is not even the root of a polynomial with rational coefficients in 1882 (basically by combining Hermites proof that this holds for e with Euler's well known equation regarding the relation of the two constants).
Compared to many others, the proofs are not that difficult, but but anybody without a couple of years of university algebra would probably find them daunting. They are certainly not/. level.
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i've been using a computer for so long that i'm half convinced that the reals are a hoax invented by physicists to make their sums easier ;-)
Well, at least you are, or rather were, in good company. When Lindemann proved the transcendence of pi, Kronecker asked:
"Of what use is your beautiful investigation of pi? Why study such problems when irrational numbers do not exist?"
That pi is irrational was first proved by Johan Heinrich Lambert in 1761, and there are a whole bunch of other proofs for it since then. The final nail was placed by Lindemann who proved that pi is not even the root of a polynomial with rational coefficients in 1882 (basically by combining Hermites proof that this holds for e with Euler's well known equation regarding the relation of the two constants).
/. level.
Compared to many others, the proofs are not that difficult, but but anybody without a couple of years of university algebra would probably find them daunting. They are certainly not