360

In English idiom a '180' is a complete reversal and a '360' is a return to where you started, because a half-turn faces you the other way and a full turn does not. The two are frequently confused, with '360' used to mean a change of mind — which says the opposite of what is intended. The skateboarding and snowboarding usage is literal rather than figurative: a 360 there is one full rotation, and the numbers continue to 540 and 720.

The Egyptian civil calendar ran twelve months of thirty days — 360 in total — and then appended five epagomenal days outside the month structure to reach 365. Several Mesopotamian administrative calendars used a 360-day schematic year for the same reason: a year of twelve equal months is far easier to compute interest, rations and rotas against than the real one. The convention survives in finance, where the 30/360 day-count basis still prices some bonds as though every month had thirty days.

The 360-degree circle derives from Babylonian sexagesimal counting and an approximate year length. Mathematics prefers radians; every practical instrument still uses degrees.

The 360-degree circle is widely believed to derive from the Babylonian sexagesimal (base-60) number system, combined with an approximate 360-day count used in some early calendars; 360's high divisor count (24 divisors) made it practical for dividing angles evenly.

There are 360 degrees around the hue wheel (worldwide, HSL and HSV colour models). Red sits at 0 and again at 360, which is the point: hue is circular, so a colour model that treats it as a line gets the wrap-around wrong.

Longitude divides the Earth into 360 degrees east and west of the Greenwich meridian, which is what ties the circle to the clock: 360 degrees against 24 hours gives exactly 15 degrees of longitude per hour, and that ratio is the basis of both time zones and the celestial navigation that preceded them. Establishing longitude at sea was for centuries a problem of carrying accurate time rather than of measuring angles.

Walk once around the outside of any convex polygon and the turns you make total exactly 360°, whether it has three sides or three hundred. This is why a regular polygon's exterior angle is 360 divided by the number of sides, and why the interior angles then follow — a pentagon turns 72° at each corner, so its interior angle is 108°. The result holds for any closed convex path, which is the reason it is stated about polygons in general rather than proved case by case.

360 = 2³ × 3² × 5, which gives it 24 divisors — more than any smaller number, making it highly composite. That is the whole practical argument for dividing the circle this way: 360 splits evenly into halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths and twelfths without ever leaving a fraction of a degree. 100 would give 9 divisors and 400 would give 15.

'360-degree feedback' names an appraisal method that gathers assessments from a person's managers, peers and direct reports rather than from a line manager alone, the figure standing for coverage from every direction. The term dates from personnel practice of the 1990s and is now standard vocabulary in human-resources work. It is a metaphor built on the full turn, not a measurement.