History
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, that follows through the ecliptic path over the course of the year, seems to advance in that path by approximately one degree, each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The Mayans used 20 cycles of 18 plus 5 unlucky days in one of their Maya calendars. 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 earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.
Aristarchus of Samos and Hipparchos seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes (DIO 14 ‡2 p. 19 n.24). Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.
The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda:
Twelve spokes, one wheel, navels three.
Who can comprehend this?
On it are placed together
three hundred and sixty like pegs.
They shake not in the least.
— Dirghatamas, Rigveda 1.164.48
Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors, making it one of only 7 numbers that have more divisors than any number twice itself (sequence A072938 in OEIS). Furthermore, it is divisible by every number from 1 to 10 except 7. This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.
Finally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.
It should be considered that if you hold your hands out at arms length and stack them from horizon to zenith there are 9 hands. The full circle is 36 hands which when divided in decimal will give 360 divisions in a circle for 360 degrees.
Read more about this topic: Degree (angle)
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