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This is by far one of the most challenging and popular HSM questions on the Net. Proofs are, countless discussions about it in math forums. The answers only led to two theories, which Wikipedia does a great job at summing up.

The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The use of a calendar with 360 days may be related to the use of sexagesimal numbers.

Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system.

The two theories seem very legitimate. With some background search I came up with the fact that the use of astrolabes by Persian astronomers (which used circles as its fundamental "measurement medium") could actually lead to invention of such system by them.

Nevertheless, Babylonians are known to be the inventors of sexagesimal system and additionally, their more "recent" studies were using such system in the advent of trigonometry.

A deeper study also indicates that Persian people could've actually be influenced by Babylonian "culture" to make use of their sexagesimal system. This makes logical decision harder: Maybe it was Babylonians who invented 360 degrees in a circle, or it could be Persians that did so with the sexagesimal system that was introduced to them.

Unfortunately, I'm not able to cite my non-English sources, but it would be great to hear an expert's advice on this.

Who were the first to use degrees in a circle and divide it to 360 parts?

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    $\begingroup$ 360 has 24 divedends. So it rather accepted by many scientists and mathematicians that we could prefer 360 degrees.Though 24 dividends are very helpfull for other calculations people on those managements side also accpeted. $\endgroup$
    – Khawaja
    Commented Apr 13, 2018 at 7:09

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We have Babylonian astronomical texts going back at least to 2000 BC. The history of Babylonian astronomy is thus very well documented. They divided the ecliptic into 360 degrees, and each degree into 60 minutes, etc. Why 360? It is true that the solar year is very approximately 360 days, though it could be noted that the Babylonians used a luni-solar year, and thus had an average of 354 days in a common year, and 383-4 in an intercalated year. The number 360 has lots of factors; in particular 360 degrees can easily be divided into 12 zodiacal signs of 30 degrees each, corresponding to the approximate position of the sun in 12 lunar months.

The results of Babylonian astronomy were adopted by the Greeks in the classical period and the division of the ecliptic into 360 degrees was adopted notably by Ptolemy in his Almagest, the most influential astronomical book in late antiquity and the middle ages. It is likely that some Babylonian mathematical knowledge passed to the Persians in the pre-Islamic period, although this is difficult to document. What is certain is that the translation of Ptolemy’s Almagest into Arabic in the 9th century made Ptolemaic astronomy well-known to learned people in the Islamic world, including Persia.

You talk about Persian astrolabes, but you do not make it clear what period you are talking about. There is no evidence for astrolabes in Persia before the Islamic period.

By the way, Wikipedia is wrong to suggest that the ancient Persians - or indeed anyone - had a year of exactly 360 days. This is an old myth. If you have access to jstor you can read about the ancient Persian calendar here: http://www.jstor.org/discover/10.2307/4299943?sid=21105210724371&uid=2&uid=2129&uid=3738032&uid=70&uid=4

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  • $\begingroup$ +1, but the link you gave me was giving "page loading error". btw, An "ancient" astrolabe was believed to belong to the era of Parthians. (that is, almost 300 years before Islam) Unfortunately, I didn't find relevant info on the Net. $\endgroup$
    – M.A.R.
    Commented Jan 30, 2015 at 15:47
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    $\begingroup$ Try this one: www.jstor.org/stable/4299943 $\endgroup$
    – fdb
    Commented Jan 30, 2015 at 15:54
  • $\begingroup$ Thanks, it worked. Though I was aware that Persian calendar wasn't 360 days. The article had this implication on me that "Persian calendar is approximately 360 degrees. And every day Earth advances approximately one degree in its course around the sun." My bad. $\endgroup$
    – M.A.R.
    Commented Jan 30, 2015 at 16:14
  • $\begingroup$ Boyer writes in his book: "It is not known just when the systematic use of the 360° circle came into mathematics, but it seems to be due largely to Hipparchus in connection with his table of chords. It is possible that he took over from Hypsicles, who earlier had divided the day into 360 parts, a subdivision that may have been suggested by Babylonian astronomy." archive.org/stream/AHistoryOfMathematics/… Evans writes "Hypsicles's is the earliest known Greek work to use the degree, a Babylonian unit of measure." $\endgroup$
    – Conifold
    Commented Feb 6, 2015 at 23:36
  • $\begingroup$ @Conifold I do not quite see why the Babylonian practice does not count as "systematic". $\endgroup$
    – fdb
    Commented Mar 1, 2015 at 23:28
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The base 60 system of the Babylonians requires 360 degrees for a full circle as a matter of ease of handling. Anything else would be inconvenient.In the base 10 system 1,2,5,10...sequence is most useful. Similarly, in the sexagesimal system, 1,2,6,36,60..will be most useful.

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  • $\begingroup$ Any multiple of 60 will do. But 60 is too course, 120 is better, 180 better still. What we need is something fairly refined to begin with and submultiples thereof. 1/60 is natural in the sexagesimal system and therefore minute = 1/60 degree, second = 1/60 minute is a good choice. The choice of full circle = 360 deg, min=1/60deg, sec=min/60 is a good choice. 5times 60 is improper in the sexagesimal system. $\endgroup$
    – Partha Shakkottai
    Commented Jul 22, 2019 at 0:23

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