My (robphy) reply to Cato11's "Acceleration through curved paths" ( https://www.physicsforums.com/threads/acceleration-through-curved-paths.1008025/ )[br][br]4 points on a circle. Three curves (inspired by Michael Iroir's comment on https://help.geogebra.org/topic/tool-for-cubic-b%C3%A9zier-curve ). [br][br]The point for the second curve controlling the second curve's initial tangent is constrained to be on the tangent line of the preceding curve, and so forth. I used Geogebra's Length function to get the length of that curve. (One would probably like the formula or algorithm to calculate that.)[br][br]UPDATE: a constrained version is at https://www.geogebra.org/m/sxjwma2q