Thanks for starting this thread, found it interesting.
Outside of the US, we covered most of this by the 6th grade in trigonometry and by 8th grade we would be working fluently with radians and degrees, the Sin rule, the Cosine rule, etc.
I never understood why one needs a computer program to calculate segments for a segmented bowl.
Using grade 7 math (overseas) for calculations including a miter saw:
Using a miter saw, for cutting segments of a segmented bowl:
Outside diameter = 15", the radius is 7.5"
If we decide to cut the pieces into 15 degree segments, we will set the miter saw precisely at 7.5 degrees, which is the angle it will actually cut into the one side of the segment.
We need a wood strip, or board approximately 1" wide.
We convert 15 degrees to radians by multiplying with Pi/180 and if we multiply that by the radius of our circle, we have the arc length (outside) of our segment.
15*Pi/180*7.5 = 1.963" which is slightly longer than what our stop should be set.
360/15 = 24, so we need 24 segments, the circumference of the bowl wil thus be 24*1.963 = 47.124"
To calculate the exact long (outside) length of the segment, for setting the stop on our miter saw, we use the Cosine rule.
a2 = b2 + c2 -2bc Cos A
b and c are the radii, while A is 15 degrees, so it follows that the exact length is 1.958"
In short, for a 15" diameter bowl (it will be slightly less than 15"), 15 degrees will give 24 segments, set the miter saw to 7.5 degrees (the angle it actually cuts onto the segment) which is half the angle of the segment it will actually cut and cut the outside length to exactly 1.958" measured with a vernier (dial) caliper.
Pure mathematics is, in it's way, the poetry of logical ideas. - Albert Einstein.