Zitat von KoRnboy91:
GAMMA, GAMMA, GAMMA HEY!
If science is, in Charles Fort's lapidary phrase, a mutilated octopus, 1/273 has to be a mutilated swastika. To see what I mean by that, take a look at these multiples of 1/7:
1/7 = 0·142857142857142857142857142857142857142857142857...
2/7 = 0·285714285714285714285714285714285714285714285714...
3/7 = 0·428571428571428571428571428571428571428571428571...
4/7 = 0·571428571428571428571428571428571428571428571428...
5/7 = 0·714285714285714285714285714285714285714285714285...
6/7 = 0·857142857142857142857142857142857142857142857142...
An obvious pattern is that each multiple is a cyclic permutation of the digits 142857; a less obvious one is that each multiple forms part of a "digital pair" in which the two numerators add up to 7: 1/7 and 6/7 are the first pair, 2/7 and 5/7 the second, 3/7 and 4/7 the third:
1/7 = 0·142857142857142857142857142857142857142857142857...
+6/7 = 0·857142857142857142857142857142857142857142857142...
7/7 = 0·999999999999999999999999999999999999999999999999...
2/7 = 0·285714285714285714285714285714285714285714285714...
+5/7 = 0·714285714285714285714285714285714285714285714285...
7/7 = 0·999999999999999999999999999999999999999999999999...
3/7 = 0·428571428571428571428571428571428571428571428571...
+4/7 = 0·571428571428571428571428571428571428571428571428...
7/7 = 0·999999999999999999999999999999999999999999999999...
This means that, given any digit in one half of a digital pair, you just subtract it from 9 to find the corresponding digit in the other half of the pair: for every 1 in 1/7, there is an 8 in 6/7; for every 2, a 7; for every 4, a 5; for every 5, a 4; for every 7, a 2; and for every 8, a 1. This also means that you can create a symmetrical pattern from the multiples of 1/7 by replacing each pair of corresponding digits with one or another of two symbols. For example, if you replace 1 and 8 with , 2 and 7 with , and 4 and 5 with as well, you get this:
1 / 7 = 0· 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 ...
2 / 7 = 0· 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 ...
3 / 7 = 0· 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 ...
4 / 7 = 0· 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 ...
5 / 7 = 0· 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 ...
6 / 7 = 0· 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 ...
The pattern isn't a very interesting one, but the reasoning used to find it applies to other reciprocals: 1/273, for example:
129/273 = 0·472527472527472527472527472527472527472527472527...
130/273 = 0·476190476190476190476190476190476190476190476190...
131/273 = 0·479853479853479853479853479853479853479853479853...
132/273 = 0·483516483516483516483516483516483516483516483516...
133/273 = 0·487179487179487179487179487179487179487179487179...
134/273 = 0·490842490842490842490842490842490842490842490842...
135/273 = 0·494505494505494505494505494505494505494505494505...
136/273 = 0·498168498168498168498168498168498168498168498168...
137/273 = 0·501831501831501831501831501831501831501831501831...
138/273 = 0·505494505494505494505494505494505494505494505494...
139/273 = 0·509157509157509157509157509157509157509157509157...
140/273 = 0·512820512820512820512820512820512820512820512820·..
141/273 = 0·516483516483516483516483516483516483516483516483...
142/273 = 0·520146520146520146520146520146520146520146520146...
143/273 = 0·523809523809523809523809523809523809523809523809...
144/273 = 0·527472527472527472527472527472527472527472527472...
In each digital pair here, the two numerators add up to 273:
129/273 = 0·472527472527472527472527472527472527472527472527...
+144/273 = 0·527472527472527472527472527472527472527472527472...
273/273 = 0·999999999999999999999999999999999999999999999999...
130/273 = 0·476190476190476190476190476190476190476190476190...
+143/273 = 0·523809523809523809523809523809523809523809523809...
273/273 = 0·999999999999999999999999999999999999999999999999...
131/273 = 0·479853479853479853479853479853479853479853479853...
+142/273 = 0·520146520146520146520146520146520146520146520146...
273/273 = 0·999999999999999999999999999999999999999999999999...
As with the multiples of 1/7, if you replace each pair of corresponding digits by one or another of two symbols, you get a pattern that in this case is best seen when the multiples are rotated through 90°... And there, a mutilated swastika -- or rather, a mirror-pair of mutilated swastikas. An infinitely repeating mirror-pair, too:
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8
/ / / / / / / / / / / / / / / / / / / / / / / /
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
= = = = = = = = = = = = = = = = = = = = = = = =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
· · · · · · · · · · · · · · · · · · · · · · · ·
4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5
5 6 6 6 7 7 7 8 8 9 9 9 0 0 0 1 1 2 2 2 3 3 3 4
7 1 5 8 2 6 9 3 7 0 4 8 1 5 9 2 6 0 3 7 1 4 8 2
8 5 2 8 5 1 8 5 1 8 5 1 8 4 1 8 4 1 8 4 1 7 4 1
7 3 0 6 2 9 5 1 7 4 0 6 3 9 5 2 8 4 0 7 3 9 6 2
5 8 1 4 7 0 3 6 9 2 5 8 1 4 7 0 3 6 9 2 5 8 1 4
4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5
5 6 6 6 7 7 7 8 8 9 9 9 0 0 0 1 1 2 2 2 3 3 3 4
7 1 5 8 2 6 9 3 7 0 4 8 1 5 9 2 6 0 3 7 1 4 8 2
8 5 2 8 5 1 8 5 1 8 5 1 8 4 1 8 4 1 8 4 1 7 4 1
7 3 0 6 2 9 5 1 7 4 0 6 3 9 5 2 8 4 0 7 3 9 6 2
5 8 1 4 7 0 3 6 9 2 5 8 1 4 7 0 3 6 9 2 5 8 1 4
4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5
5 6 6 6 7 7 7 8 8 9 9 9 0 0 0 1 1 2 2 2 3 3 3 4
7 1 5 8 2 6 9 3 7 0 4 8 1 5 9 2 6 0 3 7 1 4 8 2
8 5 2 8 5 1 8 5 1 8 5 1 8 4 1 8 4 1 8 4 1 7 4 1
7 3 0 6 2 9 5 1 7 4 0 6 3 9 5 2 8 4 0 7 3 9 6 2
5 8 1 4 7 0 3 6 9 2 5 8 1 4 7 0 3 6 9 2 5 8 1 4
4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5
5 6 6 6 7 7 7 8 8 9 9 9 0 0 0 1 1 2 2 2 3 3 3 4
7 1 5 8 2 6 9 3 7 0 4 8 1 5 9 2 6 0 3 7 1 4 8 2
8 5 2 8 5 1 8 5 1 8 5 1 8 4 1 8 4 1 8 4 1 7 4 1
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das kommt raus, wenn mans bei google eingibt
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