mercredi 10 juin 2015

Mule !!!


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Mathématiques expérimentales

http://fr.wikipedia.org/wiki/Math%C3%A9matiques_exp%C3%A9rimentales

http://fr.wikipedia.org/wiki/Platonisme_math%C3%A9matique

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mardi 9 juin 2015

Euler

\sum_{n=1}^\infin \frac1{n^2} =\frac{\pi^2}6

On constatera que la convergence vers p (n de 1000 en 1000) est assez lente : 3,14159... n'est atteint que pour n = 360 000. L'usage de séries en 1/na n'est jamais très efficace en termes de rapidité de convergence. On utilise de préférence des séries en xn avec 0 < x < 1; un exemple convaincant est le calcul de p par la formule de Machin.

http://fr.wikipedia.org/wiki/Probl%C3%A8me_de_B%C3%A2le

http://fr.wikipedia.org/wiki/Fonction_z%C3%AAta_de_Riemann

\zeta(2) = \frac{\pi^2}{6} \quad ; \quad \zeta(4) = \frac{\pi^4}{90} \quad ; \quad \zeta(6) = \frac{\pi^6}{945}\quad ; \quad \zeta(8) = \frac{\pi^8}{9450} \quad ; \quad \dots

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mercredi 3 juin 2015

3*pi en fraction continue 

[9; 2, 2, 1, 4, 1, 1, 1, 97, 4, 1, 2, 1, 2, 45, 6, 4, 9, 1, 27, 2, 6, 1, 4, 2, 3, 1, 3,
1, 15, 2, 1, 1, 2, 1, 1, 2, 32, 1, 9, 2, 1, 1, 3, 2, 1, 1, 1, 19, 2, 1, 25, 10, 2, 1,
1, 2, 1, 38, 1, 11, 1, 1, 2, 1, 1, 9, 1, 1, 1, 1, 17, 4, 2, 1, 3, 2, 2, 1, 50, 1, 53,
137, 1, 6, 1, 9, 16, 75, 4, 1, 4, 5, 3, 2, 16, 1, 1, 1, 3, 27, 1, 1, 7, 2, 8, 1, 1, 1,
1, 5, 1, 2, 6, 14, 8, 1, 1, 1, 3, 3, 5, 2, 2, 13, 3, 22, 3, 175, 1, 5, 1, 1, 1, 2, 1,
2, 6, 4, 2, 5, 1, 11, 2, 2, 1, 9, 1, 1, 4, 1, 9, 1, 4, 2, 2, 1, 1, 9, 1, 4, 1, 1, 3, 1,
3, 1, 10, 2, 39, 1, 2, 3, 2, 9, 3, 3, 2, 3, 62, 1, 4, 1, 1, 1, 4, 1, 1, 3, 3, 1, 1, 1,
1, 16, 1, 39, 2, 6, 2, 1, 1, 7, 1, 1, 1, 4, 1, 11, 2, 1, 1, 1, 5, 4, 66, 6, 2, 2, 1, 2\
0, 1, 2, 1, 41, 1, 2, 4, 2, 1, 1, 3, 1, 39, 2, 2, 1, 2, 1, 1, 5, 1, 1, 1, 2, 2, 5, 1, 5,
1, 9, 10, 1, 3, 4, 1, 4, 1, 2, 5, 3, 2, 2, 1, 2, 10, 1, 3, 1, 1, 1, 1, 4, 1, 23, 1, 2,
1, 1, 3, 2, 2, 1, 1, 2, 3, 1, 1, 1, 1, 15, 1, 2, 5, 3, 1, 2, 1, 1, 7, 1, 1, 1, 11, 12,
9, 16, 6, 1, 5, 1, 1, 2, 1, 3, 145, 2, 1, 2, 4, 3, 1, 5, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1,
1, 2, 3, 2, 2, 3, 7, 16, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1,
3, 2, 1, 7, 2, 2, 2, 1, 16, 16, 1, 1, 1, 1, 4, 1, 2, 3, 8, 1, 2, 1, 1, 19, 17, 5, 6, 4,
1, 1, 1, 49, 2, 2, 2, 1, 1, 14, 7, 2, 1, 5, 6, 1, 30, 2, 3, 2, 4, 1, 10, 1, 3, 1, 7, 3,
1, 7, 1, 1, 3, 2, 2, 3, 15, 4, 9, 1, 65, 4, 11, 1, 1, 4, 1, 2, 1, 4, 1, 1, 1, 1, 134,
2, 2, 6925, 4, 1, 5, 1, 1, 7, 1, 1, 1, 2, 8, 1, 30, 1, 2, 18, 5, 6, 2, 1, 97, 1, 1, 4\
5, 1, 6, 3, 1, 16, 6, 5, 2, 1, 1, 4, 14, 2, 11, 3, 2, 1, 3, 7, 1, 1, 4, 7, 9, 1, 1, 42,
1, 1, 131, 2, 3, 2, 1, 2, 2, 1, 1, 1, 5, 8, 1, 1, 6, 6, 2, 1, 1, 1, 23, 1, 3, 8, 1, 21,
3, 1, 9, 1, 3, 6, 5, 1, 4, 11, 21, 6, 1, 1, 1, 6, 11, 2, 6, 1, 3, 2, 1, 2, 4, 8, 2, 1,
4, 1, 1, 1, 6, 1, 4, 1, 35, 1, 2, 1, 2, 1, 3, 4, 2, 2, 83, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2,
1, 1, 2, 8, 1, 1, 11, 6, 1, 48, 1, 11, 2, 2, 4, 4, 7, 2, 4, 35, 2, 9, 2, 1, 1, 3, 1, 2,
3, 23, 5, 1, 26, 2, 1, 15, 1, 8, 2, 2, 7, 1, 1, 1, 5, 1, 4, 1, 2, 1, 3, 20, 2, 39, 2,
1, 2, 1, 1, 4, 8, 7, 2, 1, 1, 2, 52, 1, 7, 1, 1, 2, 1, 1, 1, 7, 3, 1, 22, 1, 1, 1, 1, 1,
9, 2, 2, 2, 9, 2, 3, 1, 1, 11, 1, 46, 1, 1, 3, 1, 1, 1, 2, 2, 7, 2, 2, 5, 1, 1, 1, 25,
14, 1, 93, 1, 3, 2, 2, 2, 5, 1, 2, 3, 6, 2, 1, 9, 4, 2, 2, 4, 3, 1, 1, 2, 1, 3, 2, 5, 1,
3, 6, 1, 2, 6, 3, 3, 1, 3, 1, 1, 118, 1, 1, 5, 5, 2, 1, 41, 3, 1, 1, 1, 2, 1, 1, 6, 3,
1, 1, 1, 9, 2, 34, 2, 3, 1, 4, 1, 1, 2, 3, 12, 4, 1, 41, 13, 1, 16, 1, 2, 5, 4, 1, 3,
2, 3, 1, 7, 3, 1, 1, 1, 3, 4, 1, 8, 2, 1, 26, 1, 9, 1, 3, 12, 2, 2, 4, 2, 11, 1, 2, 1,
7, 1, 2, 1, 82, 2, 2, 5, 20, 1, 39, 8, 2, 4, 38, 2, 1, 1, 1, 1, 5, 11, 3, 1, 1, 3, 17,
5, 24, 2, 1, 2, 15, 1, 1, 2, 4, 1, 3, 2, 39, 1, 3, 1, 1, 3, 1, 1, 10, 1, 5, 3, 2, 1, 2,
2, 3, 1, 18, 1, 2, 2, 1, 4, 5, 3, 4, 3, 9, 7, 2, 1, 3, 1, 5, 1, 61, 1, 1, 20, 3, 12, ...]
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