Any ideas? Strikes me It’d be easier to go with an even 400 rather than futz around with 45’s and 180’s.

Was 360 some strange standard in ancient Greece? Is the powerful protractor lobby keeping the world in the dark ages to further it’s own sinister ends?

Short answer, from the math book I’m copyediting at the moment: Some scholars attribute the use of 360 degrees to ancient civilizations that believed that 60 was a “perfect number” and that six 60s made a “perfect circle.”

I’m sure someone will be along shortly to fill in all the details.

360 has several advantages over 400. 360 is evenly divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, and so forth–many small integers. 400, OTOH, is evenly divisible only by 2, 4, 5, 8, 10, 16, 20, 25, and so forth. Thus even an equilateral triangle, one of the simplest geometric forms, cannot be given an equal number of gradians (which is the system of angle measurement in which the circle is divided into 400 parts).

Futzing around with 45’s and 180’s (which are 50 and 200 gradians, respectively) is easier than futzing with 33.3333 gradians (30 degrees), the angle for which sin(theta) = 0.5, or 66.6666 gradians for each angle of an equilateral triangle.

Now–those are answers after the fact, an explanation of why we still use the system. I do not know with certainty how it came into being. I believe it had to do with the Babylonian sexadecimal counting system: 60 seconds in a minute, 60 minutes in a degree, 6 times 60 degrees in a circle. Anyone else know for sure?

Oh yeah, I can just hear a trim carpenter say to his assistant, “cut me a piece of that quarter-round eight-six and thirteen-sixteenths, with a pi-over-four on the left end.”

That assistant would do a “pi” and get out of there!