15 Oct
2012
15 Oct
'12
10:18 a.m.
On Sun, Oct 14, 2012 at 11:45 PM, Bill Gosper <billgosper@gmail.com> wrote:
E.g., where would you put
Out[426]= 22/7 + Sin[22/7]
In[427]:= N[% - π, 2] Out[427]= 3.4*10^-10
?-) rwg
In the numerical category: The function f(x) = cot(x/2) has a 0 at pi, and by the continued fraction, 22/7 is a convergent to pi (and thus a good approximation). If you plug f(x) into Newton's method, you get the iteration: x --> x + sin(x). Admittedly the approximation that you get from this is much better than you'd expect in the generic Newton. Victor