Timeline for Extremely messy proofs
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2011 at 3:01 | comment | added | Li Zhou | We should stop crediting "the nice proof" to Niven. It rightfully belongs to Hermite. Niven's proof is a slight "variation" of Hermite's proof. The integral Niven used (a simple change of variable from Hermite's integral) is closely related to Lambert's continued fraction. Read my preprint and the references therein. | |
| Oct 29, 2010 at 1:10 | comment | added | Gerry Myerson | According to Laczkovich, On Lambert's proof of the irrationality of $\pi$, Amer Math Monthly 104 (1997) 439-443, "The last monograph that gives Lambert's argument in detail seems to be Chrystal's Algebra." | |
| Oct 28, 2010 at 16:39 | comment | added | John Stillwell | By the way, is there an accessible version of Lambert's proof? (If I remember rightly, his works are mostly in Latin and not easily available.) | |
| Oct 28, 2010 at 8:50 | comment | added | Franz Lemmermeyer | Lambert actually showed that tan x is irrational whenever x is a nonzero rational number. This is much stronger than just the irrationality of $\pi$. In addition, the proof is quite readable and well motivated, though not as polished as Niven's. | |
| Oct 28, 2010 at 6:09 | history | answered | Gerry Myerson | CC BY-SA 2.5 |