
Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted:
Aug 2, 2013 1:38 PM


On 08/02/2013 06:49 AM, Richard Tobin wrote: > In article <85ffb478968f4de69284b1e53fc19f0d@googlegroups.com>, > <jonas.thornvall@gmail.com> wrote: > >> But one 1/phi is not a rational ratio, but the 1/6 hexagon (center to >> vertex/sum of sides) is and so is all polygons derived from multiplying >> the vertices. > > You were claiming that pi is rational. It is not. > >  Richard >
This jogged my memory about Lagrange and irrational numbers. Lambert was the first to prove the irrationality of pi: in 1761,
< http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational > .
Lagrange showed that if x > 0 is rational, then sin(x) is irrational.
Ref.: (from sci.math in 2011) ====================================================================== In JeanGuillaume Garnier's "Analyse algebrique, faisant suite a la premiere section de l'algebre", 1814,
pages 538 and 539, he mentions Lagrange and C. Haros. He writes that Lagrange showed that, if x > 0 is a rational number, say x = p/q with gcd(p, q) = 1, then sin(x) is irrational.
This uses the Taylor series: <snip> ======================================================================= d.b. in sci.math, http://mathforum.org/kb/message.jspa?messageID=7364740
sin(pi) = 0 is rational. pi>0.
If we assume Lagrange's result: x>0, x rational ==> sin(x) is irrational, then we can conclude that pi must be irrational.
david
 On Hypnos, http://messagenetcommresearch.com/myths/bios/hypnos.html

