# Is a spring shaped like a sine wave?

It's just a casual observation, so I wanted to check it: A regular spring, when not completely compressed, looks an awful lot like a sine wave. The idea of a circular shape stretched out in the third dimension also seems to support it. But I can find no mention anywhere that such a spring actually is (or isn't) shapes like a sine wave. I don't want to tell my pupils this unless it is more than just an observed similarity. So is a stretched spring, if seen from the side, shaped like a sine wave?

• I don't understand the question. What do you mean by a spring being "shaped like a sine wave"? Apr 18, 2016 at 0:10
• I believe he means the projection of the spring onto a plane that cuts through the center Apr 18, 2016 at 0:11
• A "regular spring" is usually a coil spring and it is shaped like a helix. There are sine and cosine in the description of that shape, which, when seen in projection from a direction perpendicular to the axis of the spring can show up (but only approximately). Apr 18, 2016 at 0:13

$$e^{ix} = \cos x + i \sin x$$