What does 1° mean?

Question

We all know and use degrees in real life, not just in math classes(even radians). We all know that π radians=180°,a full rotation of circle equals to 360°, degrees is a measurement unit of an angle and blablabla etc... But a basic question is what does 1° represent?To What it equals to? I mean why for example full rotation of a circle equals 360° and not some other number. How it is measured?

Answer 1

I think we originally defined 1° to be the $1/360$ of a full circle, because this lets us divide the circle into many angles we use in the everyday life: $360 = 2^3 \cdot 3^2 \cdot 5$ has $24$ distinct divisors, and as you can see we can easily divide the circle into halves, thirds fourths etc without having to deal with a fractional number of degrees. The exact origin is - to my knowledge - unknow, but this seems to be one reasonable reason.

This is also why we have still systems of units that may seem strange (strange meaning not base 10), but that are quite useful for everyday life: 24 hours per day, 60 minutes per hour etc.

But there are also other conventions, depending on what area you need your measurement of angle in, see https://en.wikipedia.org/wiki/Angular_unit

Answer 2

Why do you assume 360 degrees has any significance whatsoever?

It doesn't.

But we have have to give it some value.

360 being divisible by not just 2,3,4,5 and 12 but also 8 and 9 is extremely versatile and useful.

Also, by coincidence, in astronomical/astrological and celestial navigation purposes, a year having roughly 360 days (a pure coincidence) would have convenience and (incorrectly) presumed significance.

Answer 3

The Sumerians and Babylonians used a Sexagesimal (base $60$) numeral system. When an object or quantity, such as the radius of a circle, was subdivided, it was typically broken into $60$ equal parts. Euclid IV.$15$ shows that if the circumference of a circle is divided into $6$ equal arcs, the points of division are the vertices of a regular hexagon whose sides are congruent to the radius of the circle. Since the radius is divided into $60$ parts, or degrees, each side of the hexagon also has $60$ degrees and a complete trip around the circle will pass through $6\times60$, or $360$ degrees.