A question for future reference. Sometimes ideas must gestate in my head, others can't be held back. This one is not even close to a gleam in my eyes.
It looks like segmented rings are all even numbered. If I want a 5 segment ring, do I double, or halve a 10 segment ring degrees? Or, some other method that looks like an Einstein theory on the blackboard.
I took general math all through high school, and use a calculator for all my timeses and guzzintas.
Don't ask why. But it could be cool.
Work your fingers to the bone,what do you get? - Boney Fingers. Hoyt Axton
You calculate the interior angle of any equal sided polygon by subtracting 2 from the number of sides and multiply by 180 and then divide that by the number of sides. For a pentagon: ((5-2)*180)/5 = 108°. Divide that by 2 to get the miter angle for cutting each side : 54°.
I suspect that most segmented rings are even simply for symmetric. Note that the fewer corners, the wider the pieces you make the segments from need to be (or the narrower the maximum ring can be once turned).
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.
It occurred to me that another reason besides symmetry that you don't see many odd number segmented rings may be because some of them wind up being weird angles that are difficult to set with protractors or miter gauges. For example, with 7 sides the miter angle would be 64.285714285714...° and 11 sides would be 73.636363... . Not exactly easy to set with traditional measure devices.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.
