Sobre maníacos e ninf[os] Como Lars von Trier construiu uma narrativa baseada nas séries de Fibonaci e em Der Triumph der Wasser, de César Leal
a- PRIMEIRO a série de Fibonaci:
The Fibonacci series bcdefghij-
is formed by adding the latest two numbers to get the next one, starting from 0 and 1: 0 1 --the series starts like this. 0+1=1 so the series is now 0 1 1 1+1=2 so the series continues... 0 1 1 2 and the next term is 1+2=3 so we now have 0 1 1 2 3 and it continues as follows ... k- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...
The Rule is xn = xn-1 + xn-2 where: •
xn is term number "n"
•
xn-1 is the previous term (n-1)
•
xn-2 is the term before that (n-2)
para vc ter uma idéia melhor: 1numa série dessas quando vc chegar ao # 300, a série indicará o #
300 : 222232244629420445529739893461909967206666939096499 64990979600 =
2 x 3 x 5 x 11 x 31 x 41 x 61 x 101 x 151 x 401 x 601 x 2521 x 3001 x 12301 x 18451 x 570601 x 230686501 x 87129547172401 4
2
2
2- o modelo
3- o que se pode fazer nessa progress찾o Se vc transformar a progress찾o em ret창ngulos justapostos
0:0 1:1 2:1 3:2 4:3 5:5 6:8=2 7 : 13 8 : 21 = 3 x 7 9 : 34 = 2 x 17 3
3-
4
The same happens in many seed and flower heads in nature. The reason seems to be that this arrangement forms anoptimal packing of the seeds so that, no matter how
large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the centre and not too sparse at the edges. The spirals are patterns that the eye sees, "curvier" spirals appearing near the centre, flatter spirals (and more of them) appearing the farther out we go. So the number of spirals we see, in either direction, is different for larger flower heads than for small. On a large flower head, we see more spirals further out than we do near the centre. The numbers of spirals in each direction are (almost always) neighbouring Fibonacci numbers! Click on these links for some more diagrams of 500, 1000 and5000 seeds.
E foi assim que foi pintada a Mona Lisa, sabia???
Fibonaci series
F =F F =0 F =1 n+1
n-1
+ F , if n>1 n
0 1
Lucas series
L =L +L L =2 L =1 n
n-1
n-2
for n>1
0 1
and here are some more values of L together with the Fibonacci numbers for comparison: n
n: 0 1 2 3 4 5
6
F: 0 1 1 2 3 5
8 13 21 34 55 ...
n
7
8
9
10 ...
L : 2 1 3 4 7 11 18 29 47 76 123 ... n
The Lucas numbers have lots of properties similar to those of Fibonacci numbers and, uniquely among the series you examined in the
l-
M
m- M n- M o- M p- M q-