By cheating with a Python script to move the mouse, I managed to get 99.9%. Seems difficult to get higher than that, perhaps due to the mouse position having integer coordinates.
100% perfect circle is a pure math thing and can't be achieved with drawing in any way.
Sure, but good luck pulling of a perfect octagon either, given the limitations of pen and paper.
And there's a perfectly good approximation that'll very quickly produce a theoretical heptagon with error margins less than the thickness of a pencil.
1/7 ~= 1/8 + 1/64 + 1/512 + 1/4096
(1/n = sum(1...infinity) of 1/((n + 1) ^ i)
(A perfect heptagon requires infinitely many steps.)
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Or if you want the largest octagon that fits in a given circle (octagon of a given radius).
I just worked that out with a calculator, but I'm fairly sure I worked that out empirically while bored in math class one year. My very wise teacher put me and the other bored kid way to the opposite side of the classroom from where his chalkboard was and looked the other way when we played 'squares' in class, safely out of the peripheral vision of any of the other kids. Probably the only time I ever dared 'pass notes' in class.
But you like, fall off the grid man.
Choose a corner and truncate, measure the edge length using a compass, and use that to draw the rest of the owl.
You can do it, but you end up with horizontal and vertical edges that are misaligned with the grid.
And I saw the opportunity to make a bad joke.
This bookmarklet also "only" gets 99.9%