I. EULER'S NUMBERS AND GOLDEN RATIO

Euler's numbers are e: 2,718281828459045...[1]

The starting point of this study was found as follows. When the first fifteen digits of the number "e" after the comma are subtracted from a quadrillion, the first three digits of the numbers obtained at the result are "618". Also, the golden ratio numbers include "618", too.(Remember, it is approximately 1,618) (For more information about "618" and biochemistry [6]) In fact, in the digits after "618" in the result, Euler's numbers are the same as the digits after the first three digits after the comma (281828459045).

Fibonacci series:.0,1,1,2,3,5,8,13,21,34,55... [7]

The golden ratio has the continued fractions (1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, 34/21, 55/34...etc) are ratios of successive Fibonacci numbers. [7]

The starting point of the numbers in the Fibonacci series is the Pascal triangle, which is also formed by the exponents of the eleven "11" digit. Namely, From Fibonacci series, the number of "55" is the eleventh(11) number. Another mysterious point is that if you calculate the diagonals of this triangle. the sum of the numbers in the diagonals will give you the Fibonacci sequence [1]. (1,1,2,3,5,8,13,21,34,55) [7]. Namely, the value of a row is a power of 11. [3]

Picture 1: The Pascal triangle and Fibonacci series [2] II. CALCULATION OF EULER'S NUMBERS FROM DECIMAL BASE SYSTEM (10) TO BINARY BASE SYSTEM (2) AND VICE VERSA

DECIMAL BINARY	101	210	311	4100	5101	6110	7111	81000	91001	101010
DECIMAL BINARY	111011	121100	131101	141110	151111	1610000	1710001	18	19	20
DECIMAL BINARY	2110101	22	23	2411000	25	26	2711011	28	29	3011110
DECIMAL BINARY	31	32	33	34	35100011	36100100	37	38100110	39	40
DECIMAL BINARY	41	42101010	43	44	45101101	46101110	47101111	48	49	50
DECIMAL BINARY	51110011	52110100	53	54	55	56	57	58	59111011	60
DECIMAL BINARY	61	62111110	63	64	65	661000010	67100011	68	691000101	70
DECIMAL BINARY	711000111	721001000	73	741001010	751001011	76	771001101	781001110	79	80
DECIMAL BINARY	811010001	821010010	83	841010100	85	86	871010111	88	89	90
DECIMAL BINARY	91	92	93	94	951011111	961100000	971100001	98	991100011	100

The first hundred of Euler's numbers are here:

e:2,71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746

At first, Euler's numbers of both digits after the comma was taken each time. For example, 71,82,81,82,84...and so on. Then these numbers are found in the binary number system in Table-1. (For instance, "71", 1000111 and so on). Secondly, convert these binary numbers to decimal number base (For instance, "71" 1000111; 1000=8 and

111=7). Finally, all decimal numbers are subjected to the addition process, respectively. $(8+7+2+4+2+2+17+2+4+2+5=55)$. The result of the addition is "55".

{"code_caption":[],"code_content":[{"type":"text","content":"Euler's numbers: 71 82 81 82 84\nEuler's numbers: 1000 111 10 100 10 10 10001 10 100 10 101 0\nEuler's numbers: 8 + 7 +2+4+2 +2 +17 +2+4+2 +5\nEMPTY=55\n\nEuler's numbers: 84(more) 59 04 52 35 36 02 87\nEuler's numbers: 100 111 01 11 1001 10 100 1000 11 100 100 10 10 101\nEuler's numbers: 4 +3 +2+3 +9 +2 +4 +8 +3 +4 +4 +2 +2 +5=55\n\nEuler's numbers: 87(more) 47 13 52 66 24\nEuler's numbers: 11 1011 11 11 01 1 10 100 10000 10 1 1000\nEuler's numbers: 3 +11 +3 +3+1+1+2+4 +16 +2 +1+8 =55\n\nEuler's numbers: 97 75 72 47 09 36\nEuler's numbers: 1 10000 1 100 10 11 100 1000 10 1 111 10 01 10 01 00\nEuler's numbers: 1+16+ 1 +4 +2 +3 +4 +8 +2 +1+7 +2+1 +2+1\nEMPTY=55\n\nEuler's numbers: 99 95 95 74 96\nEuler's numbers: 1 1000 11 1 01 1111 1 01 1111 100 10 10 1\nEuler's numbers: 1 +8 +3 +1+1+15 +1+1+15 +4 +2 +2 +1=55\n\nEuler's numbers: 96(more) 69 67\nEuler's numbers: 100000 100 00 101 10000\nEuler's numbers: 32 +2 +EMPTY+5 +16 =55\n\nEuler's numbers: 67(more) 62 77 24 07 66\nEuler's numbers: 11 111 110 10 01 101 1 1000 1 11 10000\nEuler's numbers: 3 +7 +6 +2+1 +7 +1 +8 +1+3+16=55\n\nEuler's numbers: 66(more) 30 35 35 47 59\nEuler's numbers: 10 111 10 1000 11 1000 11 1011 11 111 01\nEuler's numbers: 2 +7 +2 +8 +3 +8 +3 +11 +3 +7 +1 =55\n\nEuler's numbers: 59(more) 45 71 38 21 78 52\nEuler's numbers: 1 101 101 1000 111 100 110 101 01 100 11 10 11 01\nEuler's numbers: 1 +5 +5 +8 +7 +4 +6 +5 +1 +4 +3 +2 +3\n+1 =55"}],"code_language":"txt"}

Euler's numbers: 52(more) 51 66 42 74 27 46 Euler's numbers:00 1 100 11 10000 10 10 10 10 100 10 10 110 11 10 11 10 Euler's numbers:EMPTY +1+4+3 +16 +2 +2 +2+2 +4 +2 +2 +6 +3 +1+3 +2=55

Euler's numbers: 52(more)	51	66	42	74	27	46
Euler's numbers:00	1 100 11	10000 10	10 10 10	100 10 10	110 11 10	11 10
Euler's numbers:EMPTY +1+4+3 +16 +2 +2 +2+2 +4 +2 +2 +6 +3 +1+3 +2=55

IV. CONCLUSION

The most widely used number digit system today is decimal. But in this work, Euler's numbers have been converted from decimal base system to binary number base system. Interestingly, the first number of Euler's numbers is "2". Binary numbers have only two digits (0 or 1) too [5].

According to Quantum Perspective Model[4], after calculating the first hundred digits of Euler numbers after the comma, the number" 55 " (ten times) was found, especially in the Fibonacci series (0,1,1,2,3,5,8,13,21,34,55...)[7].The 11th digit in the Fibonacci series is also "55". The numbers of the this series can be reached through The Pascal Triangle with the exponents of this number 11.As a result, after calculating the first hundred of Euler's numbers after the comma, the number" 55 " has been obtained (ten times).It is the sign of the relationship between Euler's numbers and Fibonacci series.During the calculation, the "EMPTY" numbers "00' are disregarded. According to the number-based system, the number" 00 " has no value, neither in the decimal nor in the binary-based system. According to binary encoding base system, on the case of current not passing, this means 0 (zero). [8] That's why, it can be the reason of disregardence of "EMPTY" "00' numbers.

As described in the reviews by Mäkelä, and Annila, the Fibonacci sequence is for other mathematical model functions which have useful results. (Mäkelä and Annila, 2010): If Fibonacci numbers are found in Nature, Why not include them in Euler's numbers? Or is it the difference how it discovers parameters in science in terms of the quantum perspective model, especially when the relevant unit of analysis is invariant numbers?