[VA] SRC#002- Almost integers and other beasties

[Valentin Albillo]

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Hi, Gerson:

(01-02-2019 11:45 PM)Gerson W. Barbosa Wrote:  640000*x^5-768000*φ^2*x^4+3000+ln(2)=0

I only have an iPad at hand right now so running this extremely quick'n'dirty Newton on it produces the intended root of your polynomial, namely:

10 def fnf(x)=640000*x^5-768000*p^2*x^4+3000+log(2)
20 def fnd(x)=(fnf(x+0.0001)-fnf(x-0.0001))/0.0002
30 p=(1+sqr(5))/2:input x0:home
35 for i=1 to 15
40 x1=x0-fnf(x0)/fnd(x0)
50 print x1;" ";fnf(x1)
60 x0=x1
70 next i

Run

?10
8.167851990851785 14317006965.841368
6.715802401810718 4653139559.305097
5.573461555087618 1501801189.590903
4.687642795302511 477761112.5232644
4.021032838991736 147136983.11165047
3.551962197641171 41803117.36241603
3.2712995361031516 9506051.502593396
3.1593486482128053 1132110.8530623894
3.141983056899174 24349.060661761047
3.141592847539331 12.090443311217141
3.1415926535896097 0.0000030975368739971643
3.14159265358956 -3.170697671084355e-8
3.1415926535895604 -1.904654323148236e-9
3.1415926535895604 -1.904654323148236e-9
3.1415926535895604 -1.904654323148236e-9

which is a nice approximation to Pi, congrats and thanks for sharing. Perhaps it's even more accurate than what the iPad produces but right now I can't tell ...

Regards.
V
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