If our test for whether a regular polygon can tesselate with itself is whether the degrees of an individual interior angle can divide 360 to yield an integer (some examples of these integers are 6 [for equilateral triangles], 4 [for squares], and 3 [for regular hexagons]), why do circles (with interior angles each of 180) not tesselate? Looking at the problem visually, they don’t even almost tesselate and just leave a tiny gap. There are huge gaps. This doesn’t make sense to me.

My thinking was that 180 goes into 360 two times, so we should be able to put two circles at a point and have them tesselate.

Does this have something to do with three points being necessary to define a plane, and our formula suggesting that a mere two circles could work?

Is there something about curves that makes them very different from line segments joined together? I would find this intriguing, since we can get to a circle by thinking of it as a regular polygon with n sides as n goes to infinity (I think).*

I have googled this and not found explanations for why the above algorithm (Let n be number of sides. If 360/(((n-2)*180)/n) is an integer, a regular polygon of this number of sides tessalates. [Or, simplified, we could use whether 360/(180-360/n) is an integer.]) delivers an incorrect result in this case.