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I 360 degrees and the Golden Ratio

  1. Dec 21, 2016 #1
    Hi All,

    I have just found in the internet an identity showing that the Golden Ratio can be expressed as a function of the cosine of the angle of 36 degrees. It seemed to me as an important fact related to this specific angle. Had this fact, historically, any relevance to the choice of the 360 degrees standard?


    Best wishes,

    Last edited by a moderator: Dec 22, 2016
  2. jcsd
  3. Dec 21, 2016 #2


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    Gold Member

    Have you done ANY research to see where 360 degrees came from? It's not hard to do.
  4. Dec 22, 2016 #3


    Staff: Mentor

    The 360 degrees came out of mathematicians using the sexagesimal number system:


    Sexagesimal is great for doing fractional arithmetic because 60 can be factored in 2 * 3 * 2 * 5 which allows for fractionals like 1/2, 1/3, 1/5, 1/4, 1/6, 1/10, 1/12, 1/15, 1/20, 1/30, 1/60 and any combination thereof.
  5. Dec 26, 2016 #4
    I have done some research and the sexagesimal system is somewhat familiar to me, its factorization properties, anatomic origin and etc. But one of the sentences the research offered me was:
    "the origins of sexagesimal are not as simple, consistent, or singular in time as they are often portrayed." - Wikipedia

    So I am asking.
    Sorry if I disturbed you.
    Simple suggestion for you not to be further disturbed with my questions is to disregard them in a next oportunity.

    Best wishes,

  6. Dec 26, 2016 #5


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    Staff: Mentor

    36 degrees are just 1/10 of a circle. If that would have played any role in choosing the number of degrees in a circle, 10 would have been a much more natural choice. But I don't see any indication that the golden ratio would have played a role. The sexagesimal system is much older than trigonometry.
  7. Dec 26, 2016 #6


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    Science Advisor

  8. Dec 26, 2016 #7
    Ok, but not necessarily trigonometry was the body of knowledge used. Natural proportions (possibly anatomic), I would say, may have been the crucial knowledge to this connection, as they were known since long.

    Besides, the role played by number of days in a year seems, imo, to add more confusion to this discussion.

    Thank you mfb for your contribution.
    Best wishes,

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