Irrationality of pi proof


by chaoky
Tags: irrationality, proof
chaoky
chaoky is offline
#1
Dec12-12, 11:03 PM
P: 2
I was wondering about Lambert's proof of π's irrationality. Supposedly he was the first one to prove it in 1761 when he derived a continued fraction for the tangent function. Then I was reading through some of Euler's translated papers when I stumbled upon the same continued fraction in Euler's E750 paper (Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit) (English translation http://arxiv.org/abs/math/0507459). This was delivered to the St. Petersburg Academy of sciences in 1780 and Euler's derivation seems to be much simpler (based on Lagrange's binomial continued fraction) although Lambert's proof is more widely known (and a bit more involved). Do Euler's manipulation of the original continued fraction follow the modern standards of rigor? Or is there more justification needed when Euler was toying around with the fraction?
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
arildno
arildno is offline
#2
Dec13-12, 01:23 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Isn't 1780 later than 1761?
Diffy
Diffy is offline
#3
Dec18-12, 03:08 PM
P: 443
AD yes, BC no.

chaoky
chaoky is offline
#4
Dec18-12, 05:55 PM
P: 2

Irrationality of pi proof


Well, yes, although Lambert's proof is much more involved. Are there any additional justifications to Euler's manipulation of Lagrage's fraction that are needed?


Register to reply

Related Discussions
Irrationality of this number. Proof. Calculus & Beyond Homework 7
Irrationality Proof Precalculus Mathematics Homework 5
Square Root Of 2 Irrationality Proof General Math 4
proof of irrationality of sqrt(2) General Math 14
[SOLVED] Easy Proof of Irrationality of Pi General Math 7