What is the origin of the 360 degree measurement? Shanyu Ji July 6, 2015 What is the origin of the 360 degree measurement? George Cantor 1 suggested that its origin can be traced to the fact that the early Babylo- nians reckoned the year to consist of 360 days during which the sum made a complete circle round the earth. This led to be division of the circle into 360 degrees, each degree being the distance traversed by the sun in one day. The Babylonians appear to have been familiar with the fact that a chord equal to the radius of a circle can be stepped out six times round the circumference, thus dividing the circle into six sectors, each having an angle of 60◦ at the center. From “A History of π”, by Petr Beckmann, Golem Press, it provides the following pas- sage: “In 1936, a tablet was excavated some 200 miles from Babylon. Here one should make the interjection that the Sumerians were first to make one of man’s greatest inventions, namely, writing; through written communication, knowledge could be passed from one person to others, and from one generation to the next and future ones. They impressed their cuneiform (wedge-shaped) script on soft clay tablets with a stylus, and the tablets were then hardened in the sun. The mentioned tablet, whose translation was partially published only in 1950, is devoted to various geometrical figures, and states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a 57 36 number which in modern notation is given by 60 + 602 (the Babylonians used the sexagesimal system, i.e., their base was 60 rather than 10). The Babylonians knew, of course, that the perimeter of a hexagon is exactly equal to six times the radius of the circumscribed circle, in fact that was evidently 1A History of Mathematics, by J.F. Scott, Taylor & Francis LTD, London, 1969, page 10. 1 the reason why they chose to divide the circle into 360 degrees (and we are still π 25 burdened with that figure to this day). The tablet, therefore, gives ... = 8 = 3.125.” Another theory is by the facts that the angle of an equilateral triangle is 60◦, and that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit. In fact, there was no any of the Greeks in the ancient time employed the ratios which we now call the trigonometrical functions. The earliest trigonometry 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. There is one more possible motivation for 360◦ measurement: the number 360 is readily divisible: 360 = 23 · 32 · 5 has 24 divisors. It is divisible by every number from 1 to 10 except 7, which has many useful applications in calculation. 2.