Open a protractor, look at a compass dial, or consult a map: everywhere, the circle is divided into 360 degrees. This number seems self-evident, as if it were inscribed in the nature of things. Yet, nothing in pure geometry imposes 360 rather than 100 or 1000. This number is the result of a human choice, over three millennia old, and this choice was dictated by the sky.
The initial question is almost childlike: Earth rotates on its axis in 24 hours, thus defining the day. It orbits the Sun in about 365 days, describing an almost circular orbit. And a circle has 360 degrees, almost exactly 1 degree per day. Is there a link between these three observations? The answer is yes, but in an unexpected way: it is not nature that chose 360, but humanity that chose 360 inspired by nature.
It all began in Mesopotamia, between the Tigris and Euphrates, in what is now Iraq. As early as the 2nd millennium BCE, Babylonian scribes recorded their sky observations on clay tablets with remarkable precision. They used a sexagesimal numeral system, i.e., base 60. This is why we still count 60 seconds in a minute, 60 minutes in an hour, and 60 arcminutes in a degree.
These astronomer-mathematicians observed each night the Sun's progress across the celestial vault. From one night to the next, the Sun moves about 1 degree among the fixed stars, along a great circle that the Greeks would later call the ecliptic. The Babylonians noted that the Sun returned to its initial position after about 360 days, a convenient approximation of the real year (365.25 days). It was then natural, for minds accustomed to base 60 and eager to divide this perfect celestial circle, to choose 360: a number both close to the year and extraordinarily rich in divisors.
The choice of 360 is not solely due to the sky. It also owes much to mathematics. The number 360 has 24 integer divisors:
This arithmetic richness is crucial for astronomers and engineers who, without calculators, had to divide circles into equal portions by hand. Dividing a circle into 2, 3, 4, 5, 6, 8, 9, 10, or 12 equal parts always results in a whole number of degrees. No other number of comparable size offers such convenience.
It was the Greek astronomers who inherited and formalized the Babylonian system. Hipparchus of Nicaea (c. 190-120 BCE), considered the founder of positional astronomy, explicitly used the division of the circle into 360 degrees to map the stars and measure celestial positions. He was also the first to systematically subdivide these degrees into 60 arcminutes and each minute into 60 arcseconds, definitively consolidating the Babylonian sexagesimal legacy.
Claudius Ptolemy (c. 100-170 CE), in his major work the Almagest, took up and expanded this framework. The Almagest remained the reference for Western and Arab astronomy until the 16th century, thus ensuring the transmission of the Babylonian degree to all subsequent scientific civilization. This unbroken thread explains why a French engineer, a Japanese navigator, and a Brazilian architect all use the same angle of 360 degrees today.
Let us return to the initial physical question. Are the day (Earth's rotation on its axis, about 24 hours) and the year (revolution around the Sun, 365.25 days) physically linked? Astrophysicists' answer is clear: no.
These two movements have distinct origins:
The fact that the year is about 365 times the length of a day is therefore a pure geographical contingency, linked to the accidental distance at which Earth formed around its star. There is no physical mechanism that synchronizes these two time scales.
Here is the crucial point that intuition can miss. The year does not last 360 days, but 365.25 days. The degree therefore does not exactly correspond to the Sun's daily movement. In reality, the Sun moves each day by \( \frac{360°}{365.25} \approx 0.9856° \), almost, but not quite, 1 degree.
The Babylonians knew this. Their most precise astronomical tablets, such as the MUL.APIN (c. 1000 BCE), already carefully distinguished the 365-day year from the idealized 360-day year. They deliberately chose 360 as the basis for their angular system, accepting a slight approximation, because the arithmetic advantages of this number far outweighed the inconvenience of a few days' discrepancy.
| Civilization or System | Era | Circle Division | Numerical Base | Main Use |
|---|---|---|---|---|
| Babylon | c. 2000-500 BCE | 360 degrees | Sexagesimal (base 60) | Astronomy, calendar, celestial cartography |
| Greece (Hipparchus, Ptolemy) | 2nd century BCE - 2nd century CE | 360 degrees, 60 minutes, 60 seconds | Inherited sexagesimal | Positional astronomy, trigonometry |
| Medieval Islam | 8th - 15th century CE | 360 degrees | Transmitted sexagesimal | Navigation, astronomy, architecture |
| French Revolution (grade) | 1795 CE | 400 grades | Decimal (base 10) | Geodesy, topography (limited use) |
| Modern Mathematics (radian) | 19th - 20th century CE | \( 2\pi \) radians | Continuous (natural) | Analysis, physics, theoretical engineering |
| Current Universal Use | Present | 360 degrees | Babylonian sexagesimal | Navigation, cartography, architecture, astronomy |
N.B.: The radian, the SI unit for angles, is defined as the ratio of arc length to circle radius. A full turn is exactly \( 2\pi \) radians, which makes the formulas of physics and mathematical analysis more elegant than in any other angular unit. But in daily practice, the Babylonian degree reigns supreme.
Earth turns, the seasons return, and our circles have 360 degrees because astronomers, over 3,000 years ago, decided that geometry would follow the rhythm of the stars. It was not nature that imposed this number, but human intelligence that chose it by reading nature. The scribes of Babylon, armed with reeds to engrave fresh clay and their eyes fixed on the night sky of Mesopotamia, chose 360 because this number reconciled two contradictory requirements: to follow the rhythm of the sky and to lend itself easily to manual calculation.
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