The Divine Proportion : ɸ (phi) = The Golden Number = 1,618

Leonardo Guilielmi   (nicknamed Fibonnaci) lived from 1170 to 1250.  His theorum in mathematics, is still extremely relevant today. 

Basically, while trying to sort out the number of rabbits that mated in a year, he discovered a sequence of numbers, that are profoundly consistent in man, nature and animals.  Imagine, a series of numbers that literally can be seen throughout nature.
Here is the beginning of the fibonnacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…and this continues.
Each number + the next number, = the third number!  That is the fibonnacci sequence.
Fibonacci numbers can be seen throughout nature. For example, here are 13 petals on a black eyed susanL

The first 100 digits of phi are :

1,618 033 988 749 894 848 204 586 834 365 638 117 720 309 179 805 762 862 135 448 622 705 260 462 189 024 497 072 072 041

ɸ is the positive solution of the equation : x²-x = 1
it is equal to : (1+√5)/2


In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. 
F(n) = F(n-1) + F(n-2)

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 etc.

Link between Fibonacci sequence & phi : the ratio of two successive terms of the Fibonacci sequence is approaching the phi number when n is big.

>> is this the key of Nature harmony in the universe ???

http://www.etereaestudios.com

In summary, the beauty of the thing lies in the hidden links between addition and ratio of terms.

For those who are sensitive to the sacred aspects of life, we can notice :

Bible :

Exodus, Chapter 16 V18 (Moses is in the Desert with the Israelites, and his people are asking him to pray God for getting food : they are told the next morning they will find food on the sand of the desert)

     "18 And when they measured it by the omer, he who gathered much did not have too much, and he who gathered little did not have too little. Each one gathered as much as he needed."

Which is certainly a beautiful way to mention and to reach, respectively, harmony.

Quran :
16:18 If you count GOD's blessings, you cannot possibly encompass them. GOD is Forgiver, Most Merciful.

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)

2^0	2^1	2^2	2^3	2^4	2^5	2^6	2^7	2^8	2^9	2^10	2^11	2^12	2^13	2^14	2^15	2^16	2^17	2^18
1	2	4	8	16	32	64	128	256	512	1024	2048	4096	8192	16384	32768	65536	131072	262144
0	0	0	0	0	1	3	6	13	26	53	107	215	431	862	1724	3449	6898	13797
1	2	4	8	16	33	67	134	269	538	1077	2155	4311	8623	17246	34492	68985	137970	etc.
1	2	4	8	6	3	7	4	9	8	7	5	1	3	6	2	5	0	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):

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

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