Why This Number Keeps Appearing

Why a Circle Has 360 Degrees

Babylonian astronomy, a very divisible number, and the alternatives that lost.

The question

Why 360, and not 100 or 1,000?

The short answer

The 360-degree circle comes from Babylonian astronomy. The sun moves roughly one degree a day, and 360 divides evenly in an unusually large number of ways.

360 = 2³ × 3² × 5 24 divisors 12 signs × 30° 6 triangles × 60° Every whole number 1–10 divides it except 7
360 splits into 12 signs of 30°, 6 equilateral triangles of 60°, and many more whole-number parts.

What science knows

Historical Fact

Babylonian astronomers divided the zodiac into 12 signs of 30 degrees, and Greek astronomers such as Hipparchus and Ptolemy used 360 degrees, subdivided in base 60, for their tables.

The pattern

Established Mathematics

360 = 2³ × 3² × 5 has 24 divisors, including every number from 1 to 10 except 7. A circle of 360 degrees splits cleanly into halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths and twelfths.

What is still uncertain

Mixed Evidence

Historians debate how much the choice came from the year’s roughly 360 days, and how much from base-60 arithmetic. Both likely played a part.

Why humans find it interesting

Historical Fact

Other systems exist. Revolutionary France introduced the grade, 400 to a circle, to fit the metric system. Mathematicians prefer radians, 2π to a circle, because they make calculus simpler.

CUE perspective

CUE Perspective

Every astrological aspect CUE and others use, the 60° sextile or the 120° trine, is a division of this Babylonian circle.

The circle is a human choice that stuck because it works, which is a good way to think about many systems CUE draws on.

Explore next

Sources

  • Neugebauer, A History of Ancient Mathematical Astronomy (Springer, 1975)
  • Evans, The History and Practice of Ancient Astronomy (Oxford University Press, 1998)
  • Robson, Mathematics in Ancient Iraq (Princeton University Press, 2008)

Written by CUE from the sources above. Some topics were suggested by Polymath; its claims are not reproduced.