vendredi 25 octobre 2019

Jeu avec la fonction zeta (posté initialement le 21.2.2018)


C'est marrant ce que l'on obtient lorsqu'on prend les carrés des parties réelles des zéros de zêta, qu'on leur soustrait le carré de la partie réelle du premier zéro de zêta et qu'on divise ces différences par e^2pi.

e^2pi = 535.492
zeros[1] = 14.1347 au carre 199.79 auquel on soustrait 199.79 et qu'on divise par e^2pi -> 0.373097
zeros[2] = 21.022 -> 441.926 -> 0.825272
zeros[3] = 25.0109 -> 625.543 -> 1.16817
zeros[4] = 30.4249 -> 925.673 -> 1.72864
zeros[5] = 32.9351 -> 1084.72 -> 2.02565
zeros[6] = 37.5862 -> 1412.72 -> 2.63818
zeros[7] = 40.9187 -> 1674.34 -> 3.12674
zeros[8] = 43.3271 -> 1877.24 -> 3.50563
zeros[9] = 48.0052 -> 2304.49 -> 4.30351
zeros[10] = 49.7738 -> 2477.43 -> 4.62647
zeros[11] = 52.9703 -> 2805.85 -> 5.23977
zeros[12] = 56.4462 -> 3186.18 -> 5.95001
zeros[13] = 59.347 -> 3522.07 -> 6.57727
zeros[14] = 60.8318 -> 3700.51 -> 6.91048
zeros[15] = 65.1125 -> 4239.64 -> 7.91729
zeros[16] = 67.0798 -> 4499.7 -> 8.40293
zeros[17] = 69.5464 -> 4836.7 -> 9.03226
zeros[18] = 72.0672 -> 5193.68 -> 9.69889
zeros[19] = 75.7047 -> 5731.2 -> 10.7027
zeros[20] = 77.1448 -> 5951.33 -> 11.1138
zeros[21] = 79.3374 -> 6294.42 -> 11.7545
zeros[22] = 82.9104 -> 6874.13 -> 12.837
zeros[23] = 84.7355 -> 7180.1 -> 13.4084
zeros[24] = 87.4253 -> 7643.18 -> 14.2732
zeros[25] = 88.8091 -> 7887.06 -> 14.7286


Et ça continue comme ça, un peu un nombre de plus tous les 2 nombres environ, et ça, très loin (enfin, assez loin, face à l'infini, enfin, cacahuètes, quoi).

Un autre jeu, on obtient un peu pareil, cette augmentation de 1 environ un coup sur deux, au niveau de la partie imaginaire :


Une nouvelle expérience marrante : prendre les parties imaginaires des zéros de zêta et les diviser par pi*pi/4.
1 --> (0.202642,5.72859)
2 --> (0.202642,8.51991)
3 --> (0.202642,10.1365)
4 --> (0.202642,12.3307)
5 --> (0.202642,13.3481)
6 --> (0.202642,15.2331)
7 --> (0.202642,16.5837)
8 --> (0.202642,17.5598)
9 --> (0.202642,19.4558)
10 --> (0.202642,20.1726)
11 --> (0.202642,21.4681)
12 --> (0.202642,22.8768)
13 --> (0.202642,24.0525)
14 --> (0.202642,24.6542)
15 --> (0.202642,26.3891)
16 --> (0.202642,27.1864)
17 --> (0.202642,28.1861)
18 --> (0.202642,29.2077)
19 --> (0.202642,30.682)
20 --> (0.202642,31.2656)
21 --> (0.202642,32.1542)
22 --> (0.202642,33.6023)
23 --> (0.202642,34.342)
24 --> (0.202642,35.4321)
25 --> (0.202642,35.993)
26 --> (0.202642,37.4856)
27 --> (0.202642,38.3607)
28 --> (0.202642,38.8549)
29 --> (0.202642,40.0548)
30 --> (0.202642,41.0626)
31 --> (0.202642,42.0384)
32 --> (0.202642,42.7359)
33 --> (0.202642,43.4338)
34 --> (0.202642,44.9986)
35 --> (0.202642,45.3411)
36 --> (0.202642,46.3322)
37 --> (0.202642,47.1049)
38 --> (0.202642,48.1441)
39 --> (0.202642,49.1895)
40 --> (0.202642,49.8285)
41 --> (0.202642,50.3594)
42 --> (0.202642,51.6806)
43 --> (0.202642,52.5163)
44 --> (0.202642,53.1278)
45 --> (0.202642,54.1046)
46 --> (0.202642,54.6148)
47 --> (0.202642,55.9763)
48 --> (0.202642,56.633)
49 --> (0.202642,57.1953)
50 --> (0.202642,58.001)
51 --> (0.202642,59.172)
52 --> (0.202642,59.7482)
53 --> (0.202642,60.8144)
54 --> (0.202642,61.1677)
55 --> (0.202642,62.0186)
56 --> (0.202642,63.2702)
57 --> (0.202642,63.8719)
58 --> (0.202642,64.3795)
59 --> (0.202642,65.3274)
60 --> (0.202642,66.0739)
61 --> (0.202642,67.0896)
62 --> (0.202642,67.7573)
63 --> (0.202642,68.5314)
64 --> (0.202642,68.8627)
65 --> (0.202642,70.281)
66 --> (0.202642,70.8252)
67 --> (0.202642,71.509)
68 --> (0.202642,72.2936)
69 --> (0.202642,72.9174)
70 --> (0.202642,73.8457)
71 --> (0.202642,74.9268)
72 --> (0.202642,75.2204)
73 --> (0.202642,75.881)
74 --> (0.202642,76.7675)
75 --> (0.202642,77.8255)
76 --> (0.202642,78.2523)
77 --> (0.202642,79.1381)
78 --> (0.202642,79.791)
79 --> (0.202642,80.2526)
80 --> (0.202642,81.5695)
81 --> (0.202642,82.0676)
82 --> (0.202642,82.755)
83 --> (0.202642,83.2433)
84 --> (0.202642,84.2612)
85 --> (0.202642,84.9382)
86 --> (0.202642,85.7951)
87 --> (0.202642,86.4667)
88 --> (0.202642,86.9526)
89 --> (0.202642,87.6102)
90 --> (0.202642,88.7848)
91 --> (0.202642,89.4524)
92 --> (0.202642,89.7425)
93 --> (0.202642,90.7866)
94 --> (0.202642,91.1823)
95 --> (0.202642,92.1704)
96 --> (0.202642,92.947)
97 --> (0.202642,93.7222)
98 --> (0.202642,94.0209)
99 --> (0.202642,94.7124)
100 --> (0.202642,95.8597)
101 --> (0.202642,96.3645)
102 --> (0.202642,97.0882)
103 --> (0.202642,97.6935)
104 --> (0.202642,98.4126)
105 --> (0.202642,98.9182)
106 --> (0.202642,100.161)
107 --> (0.202642,100.552)
108 --> (0.202642,101.148)
109 --> (0.202642,101.733)
110 --> (0.202642,102.565)
111 --> (0.202642,103.472)
112 --> (0.202642,103.907)


Aucun commentaire:

Enregistrer un commentaire

Comme un éléphant dans un magasin de porcelaine

https://m.youtube.com/watch?v=h_aC8pGY1aY