360 degrees and the Golden Ratio

  • #1
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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?

(https://en.wikipedia.org/wiki/Golden_ratio)

Best wishes,

DaTario
 
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Answers and Replies

  • #2
phinds
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Hi All,

I have just found in the internet an identity showing that the Gonden Ration can be expressed as a function of the cossine 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?
Have you done ANY research to see where 360 degrees came from? It's not hard to do.
 
  • #3
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The 360 degrees came out of mathematicians using the sexagesimal number system:

https://en.wikipedia.org/wiki/Sexagesimal

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.
 
  • #4
893
26
Have you done ANY research to see where 360 degrees came from? It's not hard to do.
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,

DaTario
 
  • #5
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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
893
26
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.
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,

DaTario
 

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