Is there a mathematical reason why the root of cos(x)=x is very close to r=exp(ln(pi/160)/13); (r and cos(r) differ by ~4x10^-7), or is it just a coincidence? Thanks, Leo
On 25/08/2014 05:56, Leo Broukhis wrote:
Is there a mathematical reason why the root of cos(x)=x is very close to r=exp(ln(pi/160)/13); (r and cos(r) differ by ~4x10^-7), or is it just a coincidence?
<handwave>It doesn't seem like the number of bits of agreement is any bigger than the number of bits you needed to specify the number, so I expect it's just coincidence.</handwave> -- g
Hello, Yes, this is the argument, the length of the proposed approximation is about the length in number of digits of precision. Just a coïncidence, and there are others, very few can be explained fully. here are a few of them : http://mathworld.wolfram.com/AlmostInteger.html http://fr.wikipedia.org/wiki/Nombre_presque_entier (in french), http://en.wikipedia.org/wiki/Almost_integer Simon Plouffe
participants (3)
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Gareth McCaughan -
Leo Broukhis -
Simon Plouffe