DNA spiral as a Golden Section

The DNA molecule, the program for all life, is based on the golden section.  It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.

Construction of the golden section, based on phi, the golden ratio
DNA and phi, the golden proportion, in the dimensions of its spirals
34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.

B-DNA has spirals in phi proportions

DNA in the cell appears as a double-stranded helix referred to as B-DNA.This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms.

B-DNA major and minor grooves in phi or golden ratio proportion

Insight on B-DNA proportions contributed by Melih Yazici.

The DNA cross-section is based on Phi

It has been reported but not yet confirmed by this site that a cross-sectional view from the top of the DNA double helix forms a decagon:

Top view of DNA molecule

A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon.

Pentagons are based on phi, the golden ratio

Construction of a decagon using two pentagons based on phi, the golden ratio

The ratio of the diagonal of a pentagon to its side is Phi to 1.  So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!


    • Perk Cartel says

      I am in awe at the need to believe that the amazing intricacy in the cosmos was created by an imaginary entity invented by story telling humans.

      • says

        I think we can all agree that imaginary entities do not create anything. If God is our Creator though, then He is not imaginary. Just to have this exchange of thoughts, we type away at computers dependent upon sophisticated programming codes, communication networks and power sources that took highly intelligent human beings centuries of purposeful design to achieve. A single strand of our DNA though contains a more sophisticated code than any mankind has created. That code contains the complete instructions to create the human brain, which is far more sophisticated than any computer we’ve conceived, and the neural networks that allow your eyes to see, your brain to think and your fingers to type. I am in awe at the need of other story telling humans to believe that the amazing intricacy in the cosmos happened without intelligence, thought and design, completely by chance and with absolutely no purpose.

        • Thomas says

          Gary, Your study on Phi Fibanacci has fascinated me for weeks, however your views on DNA is rather brief leaving much to be desired, are there any sources you might know of to further my knowledg?? Good work by the way!

      • Jax says

        Are you also in awe that imaginary value for an idea called money allows people to rationalise people dying, losing their integrity, their happiness and it has given an imaginary idea that a selected few’s lives (financially elite)means more than even an entire continent (Africa for example). Does it also make sense that men and women are being sent the front lines to fight a war for corporate profits, so humans can play god and kill and make others in doing so, but there can’t be a god that loves all and is beyond all ego and fear?

      • says

        This is why Atheists are so undesirable to have around. I’d rather have a dinner with people of various theistic beliefs (extremists notwithstanding)… people who are polite and respectful enough of other folks to not constantly point out that their beliefs are wrong.

        Here’s a lesson to improve your social interactions:
        If you don’t believe in a God, fine. Every time a theist brings up God, subtly roll your eyes at the comment, don’t draw any more attention to the comment, and move on.

        • Per Mathisen says

          I wander why “theists” always postulate that complicated structures must have been created by one great God. Why couldn´t it have been a team of smaller gods ? Almost all complicated devices like an android phone are created by lots of people working together.
          And still, if our world is a one-man-show – how can we know that this God is still alive and active ?

          • says

            It’s not just that “theists postulate” but that mankind’s most significant experiences with the supernatural have revealed a God who says He is One. This is the foundation of all MONOtheistic religions, and found throughout their scripture. The first of the Ten Commandments includes “I am the Lord your God … You shall have no other gods before me.” Deuteronomy 6:4 proclaims, “Hear, O Israel: The LORD our God, the LORD is one.” Jesus affirms this as the most important commandment in Mark 12:29. Mohammed brings the same message. As to knowing that God is alive and active, ask those who follow Him in faith for the evidence in their own lives. We each must seek God to know the reality of that experience on a personal level, but as Jesus said in Matthew 7, “Ask and it will be given to you; seek and you will find; knock and the door will be opened to you. For everyone who asks receives; the one who seeks finds; and to the one who knocks, the door will be opened.” That’s how you can know.

          • Per Mathisen says

            Thank you for your ”religious” proof of God´s existence. But my concern was something else – the lack of logic in the argument that there must be just one almighty creator, God, because of the tremendous complexity of living material. At least, I don´t see the logic. To believe or not to believe in God is quite another issue.

          • says

            Good point. You’re quite right that life has tremendous complexity, and the existence of more than one Creator in the creation process is certainly a logical possibility. To extrapolate on your example on lots of people working together on human projects, there’s most often one person who is the visionary, the driving creative force or at least the decision maker when options or conflicts are encountered in the process. Lots of people were involved in bringing the iPhone to reality, but most would acknowledge that Steve Jobs’s role was not that of just one of many humans on the team. From a logical and a spiritual perspective, we would be created in the image of our Creator(s) and would likely function in many of the same ways.

      • Agnes says

        Why people like you, Perk Cartel, feel the need to push their opinions upon others’ beliefs using hateful sarcasm eludes me. Your statement proves nothing except that you do not actually think very deeply. Use that intricate brain of yours, silly human.

  1. Eyal Schwartz says

    I was ever so pleased to find the coherent explanation regarding phi and the DNA structure. I am writing my fourth fiction novel nowadays and am looking for material about DNA to assist me with background to the story I’m creating.
    Many thanks
    Happy new year

  2. Andrea says

    This is incredible. I can’t tell if this is the result of someone just picking a number and going around finding examples of it, or if it’s actually some weird

  3. says

    Revelation 21 is giving us a hint of the shape of the DNA.

    Revelation 21
    27 And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb’s book of life.

    The book of life is the DNA, so it’s interesting that two Fibonacci numbers stand out in this chapter. The number of the chapter (21) and the number 144 in verse 17 are both Fibonacci numbers. The Fibonacci numbers form the Golden spiral or Phi spiral, which is the shape of the book of life.

    17 And he measured the wall thereof, an hundred and forty and four cubits, according to the measure of a man, that is, of the angel.

    The measure of a man is in Phi and angel could be an anagram for angle.

    • Rinaldo says

      For the anagram:
      Please consider that the Bible was not written in English and, at least in Greek, the two words in question are very different each other.

      • RJRansomed says

        No…it was written in Hebrew the ULTIMATE Phi language! Every letter has a color, musical note, pictograph, number and action. This means that every letter has a frequency. It goes so much deeper than what is on the surface. The Designer, as in the fractals and in mathematics, is so amazing that in order to try to understand His magnificence and wrap our minds around His essence, we can only reduce Him.

  4. Alassane says

    Hi, I am doing this project for Algebra to explain what the golden ratio has on life and I chose DNA. This site is very useful, and I didn’t have to use another source for information. I recommend this site to anyone and everyone.

  5. JEM says

    i have a project on building a double helix DNA model, and it must be greater than 50 cm tall…. all of my materials must cost less than $10…. can any one help me out?

  6. Mike Anderson says

    Could you provide me a scientific reference for the DNA being 21 angstroms in diameter? I need this for my work and all of the material I have checked thus far states b-DNA is 20 angstroms in diameter. It would be greatly appreciated. As an aside, Watson & Crick state that the distance from the P atom to the center of the helix is 10 angstroms however it appears the distance between one of the O atoms and the P atom in the phosphodiester bond then you can add ~0.5 angstroms to each side of the helix.

    • says

      A Google search shows many references to both 20 and 21 angstroms, with some about “about” as a qualifier. Your comment that the inner radius is 10 angstroms plus 0.5 to the outside (i.e., a diameter of 20 to 21) may explain both references.

  7. dylan says

    if you belive in evolution u obviously dont care about statistics. The chances of everything coming from nothing are INFINITELY low. evolution is impossible

    • ThelemaSathanas says

      and if there could be, was, and/or is a god, and he-she/it was the progenitor of evolution? what then?

      ad hoc. your statement is invalid.

  8. says

    Bienvenue, Welcome Bienvenido …  in my world of « NUMBERS in DNA and GENOMES » … Summary overview http://golden-ratio-in-dna.blogspot.fr/2015/04/april-2015-from-artificial-neural.html

    Three strong publications overview:

    Codon Populations in Single-stranded Whole … – The Shakedown
    Codon Populations in Single-stranded Whole Human Genome DNA. Are Fractal and Fine-tuned by the Golden Ratio 1.618. Jean
    Integers neural network systems (INNS) using resonance … – IEEE
    Dr Jean-claude perez
    Decoding non-coding Dna Codes: Human Genome Meta-Chromosomes …
    Ref 2: Jean-claude Perez, L’ADN DECRYPTE (DNA DECODED), (1997) Marco Pietteur publishing (Resurgence collection) Embourg Belgium, ISBN 2-87211-017-8 (in french)

    some other links :


    Scientific article to NUMBERS in DNA and GENOMES… 

    2010 : « Interdisciplinary Science » (springer verlag) article :

    Artificial Intelligence:

    25 years ago, our artificial neural net “FRACTAL CHAOS” provides “déja vu” holographic like memory from a small 3×3 fractal chaos neurons: more in:

  9. ThelemaSathanas says

    let us not withhold that the god understood by conventional theism is only a reflection-from-water. neither theists nor atheists are the wiser to whatever shadow they revere or reject, and the time for every lamentation or plea for attention (as it were for either aforementioned narrow view) is time ventured nowhere.

    418. “Thou knowest not.”

    • says

      That is why it is important that our theism be based on what God reveals to us rather than what we conceive with our diverse and very limited mortal minds. Jesus said in John 10:30 “I and the Father are one” and in John 14:7, “If you really know me, you will know my Father as well. From now on, you do know him and have seen him.” Our human minds cannot embrace all that God is, but a faith that seeks knowledge of God is going to unveil more wisdom about God than one that rejects or denies Him. In Christ’s words in Matthew 7:7, “Ask and it will be given to you; seek and you will find; knock and the door will be opened to you. For everyone who asks receives; the one who seeks finds; and to the one who knocks, the door will be opened.”

  10. V Koistinen says

    Before being in awe people should take into account that this structure is certainly functionally optimal for that chemical structure, i.e. a physical necessity. There is no reason to assume that in principle the genes could not consist of entirely different chemical structures.


  1. […] The human form is effected by it as well, in the face, body, fingers, teeth and even our DNA. Phi is also thought to affect our perceptions of beauty. Art, architecture and areas of design […]

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