Ａ sine curve coiled in a sinusoidal fashion? Hi all, I am find the mathematical representation of a wire itself is of a sinusoidal shape, and now we coil this sinusoidal shaped wire into a sinusoidal shape again, so it's like a double sine wave. I have a rough idea, that is to first define a new coordinate at each point of sine curve, the basis given by the unit tangent and unit normal vectors, and from these new basis at every point, I can define a sine curve again. But my problem/confusion is that, to do this, i have to use the arc-length as the parameter, instead of the x-coordinate, right? Can someone please enlighten me? Thanks.