[D66] [MATH] New fractional approximations for golden ratio φ found: 987/610 (!)

[René Oudeweg]

φ (Is deze al bekend? )

golden ratio = (1 + √5) / 2

{\displaystyle \varphi } 1.61803 3988749894
987/610      = 1.61803 27868852459016393442622950819672131147540984


On 2/3/24 21:44, René Oudeweg wrote:
> (Meer nieuws...)
>
>
> e            = 2.71828 18284590452353602874713526624977572...
>
> reinold at fedora:~/Projects/evenodd$ python eo.py 4000 4 1  2.71828
>
> 650/607      = 2.71828 66556836902800658978583196046128500823723229
>
>
> SQRT(2)   √2 ≈ 4756/3363
>
>                  1.414213 5623730950488016887242096980785696718
>
> reinold at fedora:~/Projects/evenodd$ python eo.py 4000 2 3 1.41421
>
> 816/577        = 1.41421 14384748700173310225303292894280762564991334
> 1492/1055      = 1.41421 80094786729857819905213270142180094786729858
> 1970/1393      = 1.41421 39267767408470926058865757358219669777458722
> 2448/1731      = 1.41421 14384748700173310225303292894280762564991334
> 2646/1871      = 1.41421 69962586851950828433992517370390165686798503
> 3124/2209      = 1.41421 45767315527387958352195563603440470801267542
> 3322/2349      = 1.41421 88165176670923797360578969774372073222647935
> 3602/2547      = 1.41421 27993718099725166862976050255202198665096192
> 3800/2687      = 1.41421 65984369184964644585039077037588388537402307
>
> 4756/3363      = 1.414213 4998513232233125185845970859351769253642581
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