>You did the math wrong. You get the right number if you divide by 2. In other words half your proportion no, that's the formula for the circumference of a circle, c=2 pi r and 75.4" isn't a proportion, it's an absolute value >Imperial is based on the Sumerian number system, base 12, which is also used to measure angles. The easiest way to divide a circle is by using whole proportions. the 360 bit came from the Babylonians who used base60, but like you said, it's a good composite number with lots of factors. But really this came from the properties of a circle and the constant pi, because 360 degrees is the same as 2.pi radians But roofers spec everything in degrees, so other than pizza I'm not sure of the point of dissecting a circle into equal proportions? Radians is more useful for calculus