You’re definitely talking about approximating a curve by drawing its tangents. I’ve done it, but have never heard another name for it.
It’s what pulykamell put up.
Is the name you’re looking for “Bézier curve”, perhaps?
*** Ponder
My art teacher called it “aestheometry.” I have no idea if that’s the right spelling, though. That’s just my best guess based on what it sounded like. I don’t recall him ever writing it down.
Yup, seems like “aestheometry” is in fact the right spelling. Wikipedia doesn’t have an entry for it, but what shows up in a Google search seems like what you’re talking about.
That’s it thetruewheel! Its is the third picture in project 6.3: Home - The Nature of Mathematics - 13th Edition
New question: To make one of those ,what would the dimensions in centimeters be if the circle had to go around a 9.5cm by 5cm square? I have no idea how to go about solving this question.
I’d have to dispute their definition of a “perfect circle.” Unless they can draw an infinite number of straight lines, they’ve got a “many sided polygon which looks a lot like a circle.”
[/picking nits]
(At least they didn’t say “literally a perfect circle.” That would have made my head explode.)
If you have a 9.5 cm x 5 cm square on you, then you will immediate get a Nobel Prize. 
I’m going to assume you meant produce a circle that touches a 9.5 x 5 cm rectangle at its four corners. But I’m not sure you’re giving enough information for that either. Couldn’t you start at any outside point and have at least some segments properly tangent? Or am I misunderstanding what you meant?
I mean the circle must be all the way around the RECTANGLE, sorry for square, it can touch the edges of the rectangle, but its not necessary, I need the minimum square to make a circle.
Seems like the same kind of method employed in String Art.
This.
Even with an infinte number of lines each quadrant converges to a parabola and not a circle.
We discussed it here.
The art aspect does seem to be called Aestheometry (not to be confused with Aesthesiometry) , but the strict mathematical term would seem to be an envelope.