JT
Posts:
1,299
Registered:
4/7/12


Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted:
Aug 2, 2013 1:52 PM


Den fredagen den 2:e augusti 2013 kl. 19:38:23 UTC+2 skrev David Bernier: > 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
Honestly i think i may have solved it alot earlier than that, problem when young is to realise who is a halfwit and who isn't.
It may have ended up with some retarded Nasa employed, i just don't know.

