has anyone ever drawn a perfect circle on an etch a sketch?
nope
nope :/
No one has ever
probably isn't as hard as you think it is. Get two servo motors, and program them to spin, one (horizontal) with v_x(t)=cos t and the other (vertical) with v_y(t)= sin t. Attach the servos, and you're good to go with a circle drawer.
Some internet hacks have you breaking the etch a sketch open, but honestly, that fine aluminum dust can make you seriously ill.
Here's an example of my (apparently old) idea in action: http://www.instructables.com/id/EtchABot-a-Versatile-CNC-Etch-a-Sketch/
pure mathematicians would say that drawing a perfect circle on anything is impossible: https://www.quora.com/Geometry-Is-it-really-impossible-to-construct-a-perfect-circle
^Exactly @jtvatsim
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