History
A circle with an equilateral
chord (red). One sixtieth of this arc is a degree. Six such chords complete the circle.
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.^{
[5]} 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.^{
[6]}^{
[7]} 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
Hipparchus seem to have been among the first
Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.^{
[8]}^{
[9]}
Timocharis, Aristarchus,
Aristillus,
Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60
arc minutes.^{
[10]}
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:^{
[11]}
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.
Another motivation for choosing the number 360 may have been that it is
readily divisible: 360 has 24
divisors,^{
[note 1]} making it one of only 7 numbers such that no number less than twice as much has more divisors (sequence
A072938 in the
OEIS).^{
[12]}^{
[13]} Furthermore, it is divisible by every number from 1 to 10 except 7.^{
[note 2]} 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.