Can Irrationality in Mathematics Be Explained by Genetic Sequences as in the Square Root of Ten? ()
1. Introduction
Prior to this study, Kevser Köklü had published articles on the Quantum Perspective Model, not only about the square of the speed of light numbers [1], but also with Pi numbers with nucleotide base coded [2]. In addition to these; Pi numbers once again extended version [3], golden ratio numbers [4], Euler numbers [5], square root of two numbers [6], square root of three numbers [7], square root of five numbers [8], square root of seven numbers [9] and Fibonacci numbers [10] were also published by Tahir ÖLMEZ. In summary, the codes of all these irrational numbers (mentioned above) explained by a genetic sequence can be found in this diagram. One of these codes is [ATAAGTCATAAGTGTATTAGTTTAAAACTG] for the square root of ten number. In sum, this paper attempts to explain whether there is a relationship between the square roots of ten and genetic codes or not? Let’s try to explain these similarities and relations of irrational numbers according to genetic sequences.
2. Methods and Discussion
2.1. Methods
In this work, the chemical formulas of nucleotide bases are calculated with regards to atomic numbers of elements. The chemical structures of bases include Carbon (C), Nitrogen (N), Oxygen (O), and Hydrogen (H). Calculation of bases with chemical atoms (See also Table 1) (Ölmez T, 2020) [4].
The atomic numbers of them: Carbon (C): 6, Nitrogen (N): 7, Oxygen (O): 8, Hydrogen (H): 1 (Wieser E M et al., 2013) [11]. The chemical structures of bases (A, T, C and G) are shown at below (Ölmez T, 2020) [4].
(A) Adenine: C5H5N5: 70; (T) Thymine: C5H6N2O2: 66, (C) Cytosine: C4H5N3O1: 64, (G) Guanine: C5H5N5O1: 78 (Lodish H et al., 2018) [12].
2.2. Discussion
First of all, a paper about Golden Ratio numbers was researched [4]. Then, according to the Quantum Perspective Model, the connection between the
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Table 1. Representation of nucleotide bases (A, T, C, G) in chemical atoms.
square root of the two [6] /three [7] /five [8] /seven [9] numbers articles were published. Nextly, the relationships between the Pi numbers [3] and Euler’s Identitiy [13] and and genetic codes were published. Now, the square root of the number ten and its genetic codes are calculated by this paper.
Based on the square root of 10, it can also be obtained as follows: the square root of two [6] is multiplied by the square root of five [8]. The genetic sequence of the square root of the two number is [GGATGACTACGGGTTTAGAAA] [6]. The genetic sequence of the square root of the five numbers is [ATTTATTCAATACATAACCCCATTGA] [8]. But the genetic sequence of the square root of the ten number is [ATAAGTCATAAGTGTATTAGTTTAAAACTG]. The common feature of these sequences is “TTT”. Now, According to Standard Dna Codon Table, it is Phenylalanine amino acid [14].
3. Calculation of the Square Root of Ten Numbers and Genetic Codes
The first three hundred digits of the square root of ten after the comma are here: The square root of 10 = 3.16227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005514854885603045388001469051959670015390334492165717925994065915015347411333948412408531692957709047157646104436925787906203780860994182837171154840632855299911859682456420332696160469131433612894979189026652954361267617878135006138818627858046368313495247803114376933467197381951318567840323124179540221830804587284461460025357757970282864402902440 [15].
At first, the first group of the square root numbers of ten after comma was taken. For example 1, 6, 2, 2, 7, 7, 6, 6, 0, 1, 6, 8, 3, 7, 9… and so on. Secondly, all decimal numbers are subjected to the addition process, respectively. (1+6+2+2+7+7+6+6+0+1+6+8+3+7+9 = 71). The sum of the first group of the root square numbers of ten after comma is “71”. Just like as in (A) Adenine: 70 (See also Table 1).
The first group of the root square numbers of ten after comma:
1+6+2+2+7+7+6+6+0+1+6+8+3+7+9 = 71 (A) Adenine: 70
The second group of the root square numbers of ten after comma:
3+3+1+9+9+8+8+9+3+5+4+4 = 66 (T) Thymine: 66
The third group of the root square numbers of ten after comma:
4+3+2+7+1+8+5+3+3+7+1+9+5+5+5+1 = 69 (A) Adenine: 70
The fourth group of the root square numbers of ten after comma:
3+9+3+2+5+2+1+6+8+2+6+8+5+7+5 = 72 (A) Adenine: 70
The fifth group of the root square numbers of ten after comma:
0+4+8+5+2+7+9+2+5+9+4+4+3+8+6 = 76 (G) Guanine: 78
The sixth group of the root square numbers of ten after comma:
3+9+2+3+8+2+2+1+3+4+4+2+4+8+1+0+8 = 65 (T) Thymine: 66
The seventh group of the root square numbers of ten after comma:
3+7+9+3+0+0+2+9+5+1+8+7+3 = 57 (C) Cytosine: 58
The eighth group of the root square numbers of ten after comma:
4+7+2+8+4+1+5+2+8+4+0+0+5+5+1+4+8 = 68 (A) Adenine: 70
The ninth group of the square numbers of ten after comma:
5+4+8+8+5+6+0+3+0+4+5+3+8+8+0+0 = 67 (T) Thymine: 66
The tenth group of the square numbers of ten after comma:
1+4+6+9+0+5+1+9+5+9+6+7+0+0+1+5+3 = 71 (A) Adenine: 70
The eleventh group of the root square numbers of ten after comma:
9+0+3+3+4+4+9+2+1+6+5+7+1+7+9 = 70 (A) Adenine: 70
The twelfth group of the root square numbers of ten after comma:
2+5+9+9+4+0+6+5+9+1+5+0+1+5+3+4+7+4 = 79 (G) Guanine: 78
The thirteenth group of the root square numbers of ten after comma:
1+1+3+3+3+9+4+8+4+1+2+4+0+8+5+3+1+6 = 66 (T) Thymine: 66
The fourteenth group of the root square numbers of ten after comma:
9+2+9+5+7+7+0+9+0+4+7+1+5+7+6 = 78 (G) Guanine: 78
The fifteenth group of the root square numbers of ten after comma:
4+6+1+0+4+4+3+6+9+2+5+7+8+7 = 66 (T) Thymine: 66
The sixteenth group of the root square numbers of ten after comma:
9+0+6+2+0+3+7+8+0+8+6+0+9+9+4 = 71 (A) Adenine: 70
The seventeenth group of the root square numbers of ten after comma:
1+8+2+8+3+7+1+7+1+1+5+4+8+4+0+6 = 66 (T) Thymine: 66
The eighteenth group of the root square numbers of ten after comma:
3+2+8+5+5+2+9+9+9+1+1+8+5 = 67 (T) Thymine: 66
The nineteenth group of the root square numbers of ten after comma:
9+6+8+2+4+5+6+4+2+0+3+3+2+6+9 = 69 (A) Adenine: 70
The twentieth group of the root square numbers of ten after comma:
6+1+6+0+4+6+9+1+3+1+4+3+3+6+1+2+8+9+4 = 77 (G) Guanine: 78
The twenty-first group of the root square numbers of ten after comma:
9+7+9+1+8+9+0+2+6+6+5+2 = 64 (T) Thymine: 66
The twenty-second group of the root square numbers of ten after comma:
9+5+4+3+6+1+2+6+7+6+1+7+8 = 65 (T) Thymine: 66
The twenty-third group of the root square numbers of ten after comma:
7+8+1+3+5+0+0+6+1+3+8+8+1+8+6+2 = 67 (T) Thymine: 66
The twenty-fourth group of the root square numbers of ten after comma:
7+8+5+8+0+4+6+3+6+8+3+1+3+4 = 69 (A) Adenine: 70
The twenty-fifth group of the root square numbers of ten after comma:
9+5+2+4+7+8+0+3+1+1+4+3+7+6+9 = 69 (A) Adenine: 70
The twenty-sixth group of the root square numbers of ten after comma:
3+3+4+6+7+1+9+7+3+8+1+9+5+1+3 = 70 (A) Adenine: 70
The twenty-seventh group of the root square numbers of ten after comma:
1+8+5+6+7+8+4+0+3+2+3+1+2+4+1+7+9 = 71 (A) Adenine: 70
The twenty-eighth group of the square numbers of ten after comma:
5+4+0+2+2+1+8+3+0+8+0+4+5+8+7+2 = 59 (C) Cytosine: 58
The twenty-ninth group of the square numbers of ten after comma:
8+4+4+6+1+4+6+0+0+2+5+3+5+7+7+5 = 67 (T) Thymine: 66
The thirtieth group of the square numbers of ten after comma:
7+9+7+0+2+8+2+8+6+4+4+0+2+9+0+2+4+4+0 = 78 (G) Guanine: 78
This sequence can be shown as [ATAAGTCATAAGTGTATTAGTTTAAAACTG]. Let me try to explain this sequence with the “Quantum Perspective Model”. For example, The first group of the square root of ten after comma equal to Adenine (A): 71 with the one more “1” Hydrogen bond (H: 1). (Remember, See Table 1; Adenine (A): 70) This result may mean the sequence of the square root of ten in groups [ATAAGTCATAAGTGTATTAGTTTAAAACTG]. The third group of the square root of ten after the comma is regarded as with the lack of one Hydrogen bond (H: 1) Adenine (A): 69; (Remember, See Table 1; Adenine (A): 70) (Because the deviations in the calculation of the square root of ten numbers can be derived from the Adenine (A)―Thymine (T) Hydrogen bonds because of Adenine (A) pairs with Thymine (T) by two hydrogen bonds. Cytosine (C)―Guanine (G) pairs with by three hydrogen bonds [16]. The reason for the lack of hydrogen bonds: Hydrogen bonding is a very versatile attraction. (Ölmez T, 2020) Hydrogen bonds are relatively weak and easily broken by increasing hardness (Farrell R E, 2010) [17]. Hydrogen Bonds are critical for the process of genetic identification and are quantum in nature (Penrose Sir Roger, 2008) [18].
4. Results
After searching the square root of the number ten with the National Biotechnology Information Center (NCBI) databases, several associations with bony fish may be found at the end of this search. What makes Danio kyathit [19] different from the others is that its strips are divided into rows of small brown spots. This fish species is closely related to zebrafish [20]. Danio aesculapii [21] is its distinguishing feature as the number of shared circular scales, which it has in common only with D. Kerri. Also Danio aesculapii, the number of dorsal fins with six branched rays, is the only example of its genus. Generally it differs from other Danio species in that it has six dorsal fins [21]. Especially, when sunlight touches the side of this fish species, it shows a variety of colors [22]. Types of bony fishes are based on Danio aesculapii (See Figure 1).
Types of bony fishes are Paramormyrops kingsleyae, Larimichthys crocea and Cyprinodon tularosa.
Types of other living creatures are birds, carnivores, rodents, eudicots, monocots, lizards, bivalves, gastropods, flatworms, beetles, moths, butterflies, walking sticks, bees, butterflies, caddisflies and flies [23] (See Figure 2).
5. Conclusion
At first, the summary of this research can be summarized as the expression of
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Figure 1. The NCBI (National Biotechnology Information Center) result for nucleotide sequence “ATAAGTCATAAGTGTATTAGTTTAAAACTG” [23].
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Figure 2. The NCBI (National Biotechnology Information Center) result blast tree view widget for “ATAAGTCATAAGTGTATTAGTTTAAAACTG” nucleotide sequence [23].
the square root of the number ten, about the first four hundred digits after the decimal point, with bases in DNA. Secondly, these found bases in DNA are scanned in the NCBI database and meaningful results are tried to be obtained. A common feature of the NCBI blasts is the result of bony fish, particularly Danio rerio (Zebra fish) (Also, See Table 2).
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Table 2. The NCBI (National Biotechnology Information Center) summary and genetic sequences of some irrational numbers.
Thirdly, Danio aesculapii has a similar appearance to Zebrafish [22] (See Figure 2). Fourthly, Since Zebra fish have the ability to regenerate heart and lateral hair cells in their larval stages; they can contribute to a replication crisis in biomedical research, providing a useful scientific model as an organism [20]. Fifthly, although there is no periodic sequence of irrational numbers, in this paper a periodic sequence has been obtained in terms of genetic sequences, just as in “AGT” and “ATA”. Remember, this sequence can be shown as [ATAAGTCATAAGTGTATTAGTTTAAAACTG]. Finally, this study may shed light on the genetic sequences to be obtained, in biochemistry not only to explain the square root of the number ten with genetic codes, but also to explain other irrational numbers with the same property.