Consider a helical segment that starts at the base of a cylinder and makes it no more than once of the way around the cylinder.
It strikes me as obvious (for whatever that's worth) that the length of this segment "corresponds to a 'wrapped' right triangle"; that is, that the length of this segment equals the length of the hypotenuse of a right triangle with legs a and b such that a's length is the length of a line segment running from the end of the helical segment along the cylinder back to the base of the cylinder, and b's length is the length from there around the base back to the starting point of the helical segment.
I expect there to be a well-known proof/theorem of this, but all I've found so far is people assuming it in making other points and others showing it or something like it with pictures/videos. Can anyone please direct me to or show me the actual mathematical proof/theorem?