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This is a question mostly about symmetry. So first off all of the lines we have confirmed,aside from the nine point circle and lines of making, are symmetrical in some way, lines of vigor and revocation, use shifting symmetry. The circle aside from nine point have both rotational and reflective symmetry. the line of silencing has rotational symmetry. Even ellipse have reflective symmetry. This feels important but I can not figure out how and it is irritating me. Thoughts and theories please.

So random thought I had while working on ellipses, they are stronger where the ellipse curves more than a circle and weak where they curve less than a circle, now noting this I realized that the curvature of a circle is relative,a circle can always have a tighter curve if it is drawn smaller. So based off this I have a theory that the larger a circle is the weaker it is. This being because of the larger a circle the less it curves. So smaller circles should be stronger based off of this reasoning. this continued to lead me to a further question. "What about Nebrask that has a massive circle and yet contains hoards of wild chalklings." Theories as to why the Circle of Nebrask is strong enough to contain a constant onslaught please.(assuming of course you agree with my theory.) otherwise thoughts and/or criticisms of the initial theory about circle strength. Also personal belief as to why this is never brought up, all of the circles we see are roughly the same size, Nebrask is faraway, and, evidently, "classified". Edit: additional thought the wider the ark the closer it is to a line of forbiddance this could theoretically give it some strength if the person got the intent right.

Spoilers This theory is about the shapes of lines of Warding. First some conic theory for the uninitiated. A conic is a shape determined by cutting a plane through two cones that meat at the point, and bases are parallel. the shapes that can be made are a parabolas, hyperbolas , ellipses, and circles. The entire theory is that a line of warding can be made by using any conic.