> Say, in the course of the manipulation of c its radius approaches
> towards infinity, and upon the radius becoming > than some Max, I want c
> to suddenly think of itself as a Line instance rather than as a Circle
> instance.
> 

Footnote:

In Fuller's synergetic geometry, circles don't become infinite lines, but
just bigger and bigger circles.  Lines that appear locally straight are just
that:  local.  Clearly we're starting with different assumptions than those
of Euclidean greek metaphysics.  More from Democritus.  Lines aren't
perfectly straight either -- zoom in and they become zig-zaggy/wavilinear.
Zoom out, and all you get are curves and great circles.

Kirby


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