by HallsofIvy » Mon Feb 10, 2020 10:02 pm
The first thing you say is that "there is no mathematical way to calculate the length of arc of a".
YES, THERE IS! An angle, with vertex on the circle, angle measure [tex]\theta[/tex] radians, subtends an arc on the circle, with radius r, of length [tex]2r\theta[/tex]. In the example you give here, the angle is 12 degrees= 0.209 radians and the radius of the circle is 60 mm. The arc subtended has length 2(60)(0.209)= 25.1 mm.