Given a point a circle with the point as its center is a set of points equidistant from the point.
Similarly given 2 points an ellipse is a set of points each with equal sums of distances from the two points.
A sine is a convergent real valued infinite series of real numbers. Plotting it in a Cartesian coordinate system interpreting its value as a coordinate on the y axis one gets a sine curve.
But was there a way to plot out an equivalent curve in a pre Descartes era, without any coordinates that is?
How to generate a sine curve with a wooden cylinder, paint and paper:
Cut the cylinder obliquely to the axis, forming a slanted elliptical "top".
Paint the remaining lateral surface.
Roll the painted cylinder onto the paper and note the boundary.