Tini Circle Groups (TCG)
Tini Circle Groups (TCG) (If no image appears below, "Click" your browser "Refresh" icon.) This post is in memoriam: René Descartes [15961650]

Curvature
I was under the impression that curvature is expressed by 1/r, with r being the circle's radius. In any case, for the pictures you posted, I'm assuming that every circle here has a radius smaller than 1, since that would be the only way for a circle to have a natural integer as its curvature (e.x., for a circle to have a curvature of 8, its radius must be 1/8, since 1/[1/8] = 8). But then if these circles thus have radii smaller than values of one, then how can epsilon exist?

Each circle has a radius that is the multiple of a common denominator.
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And, also of course, the circles of a Tini Circle Group symbolize a Natural spheroid, a Pulsoid, which is an ellipsoid; and all ellipsoids are defined by the Elliptical Constant (EC). That is to say: the “common denominator” of all TCGs is the EC, which is the heuristic symbolization of the Conceptual Unit (CU). 
I found the error . . . in the original post and corrected it.
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Amazing how once an error is made, the writer can never see it. 
Re: Each circle has a radius that is the multiple of a common denominator.
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There is a deep, common relationship among the Tini Circle Group integers . . .
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There is a deep, common relationship among the Tini Circle Group integers such that by changing any curvature integer by a single integer, or any value, the entire array collapses. (If no image appears below, "Click" your browser "Refresh" icon.) In the above diagram, I have arbitrarily chosen the adjacent, tangent curvatures of 156, 182, 254, and 1268, near the top center.The highest relationship is that when each of the selected integer numbers is squared (24,336, 33,124, 64,516, and 1,607,824) they total exactly 1,729,800. And, when the same selected numbers are added (156 + 182 + 254 + 1268) they equal 1,860. If 1,860 is squared (3,459,600) and divided by 2, it is exactly the same integer 1,729,800. The same process will yield equal integer values, regardless which four tangent circles you select. And, arrays can be constructed such that the smallest integer value of an array can be any integer. This demonstrates a complex, unique, integer, relationship between tangent circles (special ellipses) that extends to the Natural arrangement of fundamental quanta, which have an outer ellipsoidal "envelope" that becomes spherical after a relatively few pulses and subsequent compression. The "Natural arrangement" of quanta is such that there is never any "empty" space. "Space" quanta (the Dyosphere) and fundamental, Intrinsic time (FIT) redefines Einstein's spacetime. 
Re: Tini Circle Groups (TCG)
Your example Tini Cirt 84:172s looks quite similar to your third (moving) signature image. How are these arrays of circles related to Pulsoids and Resoloids?

Space is “packed” with compressed Pulsoids.
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Pulsoids have a more direct relationship to the arrays because of an analogous spheroidal geometry with an integer relationship of its major diameter to its salient structural geometry. Pulsoids are the “dark matter” “packed” quanta of space. There is no empty “space” and thus, space is “packed” with compressed Pulsoids as heuristically demonstrated with Tini Circle Groups (TCG). 
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