fri arvo selloff, page-13

re: they're switching "
You should know that degrees and days aren't equal.
360 degrees in a circle and 365/6 days in a year.
Not much difference but there it is."

At the present time JC the above is 'about right; however in eons past the Earth year has fluctuated from around 350 days in a year to 374 days in a year if my memory serves me correctly so it seems that 'those who know' took the mean (ave) no. of degrees at least in an indirect sort of way.

I'm glad you asked this question, because I've been wondering it myself. I
figured it had something to do with the Babylonians, who used a base 60
number system. But it sure took a lot of digging in several books to find
out anything concrete about it.

I finally found what I was looking for in a book called "A History of Pi" by
Petr Beckmann, a mathematician from Czechoslovakia. Here's the passage:

In 1936, a tablet was excavated some 200 miles from Babylon. Here one
should make the interjection that the Sumerians were first to make one of
man's greatest inventions, namely, writing; through written communication,
knowledge could be passed from one person to others, and from one
generation to the next and future ones. They impressed their cuneiform
(wedge-shaped) script on soft clay tablets with a stylus, and the tablets
were then hardened in the sun. The mentioned tablet, whose translation
was partially published only in 1950, is devoted to various geometrical
figures, and states that the ratio of the perimeter of a regular hexagon
to the circumference of the circumscribed circle equals a number which in
modern notation is given by 57/60 + 36/(60^2) (the Babylonians used the
sexagesimal system, i.e., their base was 60 rather than 10).

The Babylonians knew, of course, that the perimeter of a hexagon is
exactly equal to six times the radius of the circumscribed circle, in fact
that was evidently the reason why they chose to divide the circle into 360
degrees (and we are still burdened with that figure to this day). The
tablet, therefore, gives ... Pi = 25/8 = 3.125.

So that's who gave us the 360 degrees in the circle. See, assignment of
degree-measure to angles is somewhat arbitrary. Some choices are more
natural than others, though, and when you're working in base 60, 6x60 is a
pretty natural choice.

As a sidenote, the actual ratio that the Babylonians talk about is
6r/(2r*Pi) = 3/Pi, which is about 0.95493. They say it's 24/25 = .96.
And you might ask why we chose Pi as the letter to represent the
number 3.141592..., rather than some other Greek letter like
Alpha or Omega. Well, it's Pi as in Perimeter - the letter Pi
in Greek is like our letter P.