Good ol' trig: that bastion of angles and triangles is essential to calculating velocity, ... That new arc-length equation works IF a full circle is 2π units all the way around.

However, people from ancient astronomers to modern navigators calculated the arc lengths and angles of triangles on a sphere. They used special globes and instruments to make measurements and teach.

Volumes using cross-sections, the disk method, the washer method and the shell method. Arc length and surface area. Infinite series, power series, Maclaurin and Taylor series. Polar coordinates and ...