N nisde New member Joined May 17, 2018 Messages 4 May 22, 2018 #1 k(s)=s is a natural equation for a curve, but I don't know which one, and I need to draw it k -"kappa" is curvature s- is arc lenght Natural equations http://mathworld.wolfram.com/NaturalEquation.html Cesaro equation http://mathworld.wolfram.com/CesaroEquation.html

k(s)=s is a natural equation for a curve, but I don't know which one, and I need to draw it k -"kappa" is curvature s- is arc lenght Natural equations http://mathworld.wolfram.com/NaturalEquation.html Cesaro equation http://mathworld.wolfram.com/CesaroEquation.html

H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 5,117 May 23, 2018 #2 It is the "natural equation" of any curve that has smooth curvature. You would need to be given the curvature and arc length at any point to be able to identify it as a specific curve.

It is the "natural equation" of any curve that has smooth curvature. You would need to be given the curvature and arc length at any point to be able to identify it as a specific curve.

D daon2 Full Member Joined Aug 17, 2011 Messages 996 May 23, 2018 #3 k(s) = as+b defines a Cornu or Euler spiral.