tom @tomcuchta@mathstodon.xyz
been a while since I used this site!
mad props to the lagrange inversion theorem https://en.wikipedia.org/wiki/Lagrange_inversion_theorem
THE PRESTIGE:
ok so, the classical proof that
root(2) involves deriving a contradiction from the assumption that root(2) is rational.
however, there is an argument to be made that there is a difference between a number being [not rational], and actually provably belonging to the class of irrational numbers, i.e. quantifiably different in some way from every rational number.
(contd.)
playing with R for the first time
its kind of cool but strange
\[\displaystyle\lim_{R \rightarrow \infty} R \displaystyle\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} e^{it} \log\left( 1 + \dfrac{1}{Re^{it}} \right) \mathrm{d}t\]
\[ = \]
\[ \pi \]
