Tuesday, September 7, 2010

Inverse of 19 and 2^n factorization suite



The counter-part of 81 against 100 is 19 (19+81=100).
The factors series 2^n - symbolizing life, as all forms of life grow according this mathematical formula - is linked to that number, if one looks at significant digit of each term:
it retrieves the counts (or numbers) that are before the final digit of each term for adding the next term (1 of 16 adds the term 32, which gives 33, then take the 3 adds it up to 64 which gives 67, it takes 6 which will add up with 128 = 134 and 13 to 256 etc. and we are interested only in the last significant digit of the result of the addition, which is bold in the table in the last row)

2^02^12^22^32^42^52^62^72^82^92^102^112^122^132^142^152^162^172^18
12481632641282565121024204840968192163843276865536131072262144
 0
 0
 0
 0
 0
13613265310721543186217243449689813797
 1
 2
 4
 8
 16
33671342695381077215543118623172463449268985137970
etc.
124863749875136250
1
we then obtain a recurrent pattern of 18 digits:
124863749875136250
invert all the numbers (the latter first, the first last):
052631578947368421
this same pattern is found in :
1/19 = 0,052631578947368421052631578947368421 ...
Note: if we add these 18 numbers of this pattern, we get 81 (we also see that 18 is the 'mirror' of 81).
0+5+2+6+3+1+5+7+8+9+4+7+3+6+8+4+2+1 = 81

Still about 19, here is the list of division of 1 to 18 by 19 (there are always the same reason, each time slightly offset, which gives the sum of 81):

1/190,0526315789473684210526315789
2/190,1052631578947368421052631579
3/190,1578947368421052631578947368
4/190,2105263157894736842105263158
5/190,2631578947368421052631578947
6/190,3157894736842105263157894737
7/190,3684210526315789473684210526
8/190,4210526315789473684210526316
9/190,4736842105263157894736842105
10/19 0,5263157894736842105263157895
11/190,5789473684210526315789473684
12/190,6315789473684210526315789474
13/190,6842105263157894736842105263
14/190,7368421052631578947368421053
15/190,7894736842105263157894736842
16/190,8421052631578947368421052632
17/190,8947368421052631578947368421
18/190,9473684210526315789473684210
which is the characteristic of "phoenix" numbers


19 circles arrange naturaly into a perfect hexagon
Ancien "flower of life" composed of 19 imbricated circles : is this because number 19 has something to do with life ?
each crossing line adds up to 46 (4+6=10=1)
  • 19 is the secret number of 190, 190/19=10=1
  • 1 is the first digit, 9 the last digit  of the 10th Base and 1+9=10=1

2 comments:

  1. you got an explanation here http://en.wikipedia.org/wiki/Recurring_decimal

    ReplyDelete
  2. Thank you very much Kader for your kind and interesting contribution

    ReplyDelete