First things first, I'm not good at searching, but I was unable to find some question like this in the board. Second things next, English is not my first language, so sorry for any mistake in the text.
I was searching for a way to draw a circle using only a ruler and I found this: https://www.quora.com/Can-you-draw-a-circle-without-a-compass-and-only-with-a-ruler-and-a-pen (the square one).
But then one thing came to my mind, do we use limiting processes over methods like this to define some shapes in the plane?
Like we define the derivative (slope of the tangent line at a point) as the limit of the slope of the secant lines as they approximate the tangent line.
This seems like a very natural thing to be done in my point of view, even if it is just for sake of knowing if it works or not, but I could not find any example of this in practice.
To make my question more clear, I'm not at a deep level in math skills, so I don't really know a lot of things. In fact, I didn't even had a first course in analysis yet, so I'm really starting out with this new concepts.
My intent here is to find some exemples of this process in use, how it's studied, what theorys lies behind it and if it's just a thing that passed throug my mind or a really relevant concept.
In that answer they generate a curve as an envelope of lines: see the Wikipedia entry for more information. By the way: the answer given is far from being correct, as the envelope in that case is not an arc of circle (red in diagram below), but an arc of parabola (blue).