角度The Angular Degree

18° The angular degree. We undoubtedly owe to the ancient Babylonians our present division of the circumference of a circle into 360 equal parts. Several explanations have been put forward to account for the choice of this number.

Thus it has been supposed that the early Babylonians reckoned a year as 360 days, and that this naturally led to the division of the circle into 360 equal parts, each part representing the daily amount of the supposed yearly revolution of the sun about the earth. Today this explanation is discredited, since we now have evidence that the Babylonians very early knew that the year possesses more than 360 days.

Again, the early Babylonians were very likely familiar with the geometric fact that the radius of a circle can be applied exactly six times to its circumference as a chord. Then, having adopted sexagesimal division, it was natural to divide the central angles of these chords into 60 equal parts, resulting in the division of the entire circle into 360 equal parts.

Otto Neugebauer, the great scholar and authority on early Babylonian mathematics and astronomy, has proposed an interesting alternative explanation. In early Sumerian times there existed a large distance unit, a sort of Babylonian mile, equal to about seven of our miles. Since the Babylonian mile was used for measuring longer distances, it was natural that it should also become a time unit, namely the time required to travel a Babylonian mile. Later, sometime in the first millennium b.c., when Babylonian astronomy reached the stage in which systematic records of celestial phenomena were kept, the Babylonian time-mile was adopted for measuring spans of time. Since a complete day was found to be equal to 12 time-miles, and one complete day is equivalent to one revolution of the sky, a complete circuit was divided into 12 equal parts. But, for convenience, the Babylonian mile had been subdivided into 30 equal parts. We thus arrive at (12)(30) = 360 equal parts in a complete circuit.