Tangent Circles

[Epsilon=One]

Tangent Circles

Within any group of four mutually tangent Natural integer (www.101123.com/NI) circles that are within any circle, there exists no space, to the infinitesimal, that does not contain a Natural integer (www.101123/NI) curvature, diameter circle that is tangent to all of its adjacent group of three mutually tangent circles.

The formula, for four mutually tangent circles (where a, b, c, and d represent the circles' curvature), is:

a² + b² + c² + d² = (a + b + c + d)² / 2

The curvature is negative or positive depending upon whether the curvature is concave or convex.

Simply: there are multiple Natural integer (www.101123.com/NI) solutions fot the above 4 variable equation when "a" is any Natural integer (www.101123.com/NI). The equations are classified by Tini Cirts (Tangent Infinity Integer Circle Terms).

See: Tini Circle Groups (www.101123.com/TCG) (TCG) for more tangent circles.

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[ste]

The mathematics of TiniCirts, heuristically, describes the internal and external "packing" of Taisoids.
How?

a² + b² + c² + d² = (a + b + c + d)² / 2
Where is this formula derived from?

[Epsilon=One]

How?The mathematics of TiniCirts, heuristically, describes the internal and external "packing" of Taisoids because all the integer curvatures are tangent to one another.

Where is this formula derived from?This is a standard algebraic geometric formula for four tangent circles known as the Descartes' Circle Theorem (www.mathforum.org/pcmi/hstp/resources/circlepacking/paper.html).

To the best of my knowledge only Brunardot, years ago, has developed the algorithms/matrixes for integer curvature for any given integer circle curvature that endlessly converges to the infinite.

[ste]

You've reminded the readers time and time again of the applicability of Gödel's Incompleteness theorem to mathematics. However, you continue to use geometry in your model of the universe. Don't the same assertions of Incompleteness Theorem apply to your constructions as well? Aren't these algebraic derivations and geometric constructions part of the larger problem described by Kurt Gödel?

[Epsilon=One]

You've reminded the readers time and time again of the applicability of Gödel's Incompleteness theorem to mathematics. However, you continue to use geometry in your model of the universe. Don't the same assertions of Incompleteness Theorem apply to your constructions as well? Aren't these algebraic derivations and geometric constructions part of the larger problem described by Kurt Gödel?No. That is because all my mathematics begins with a provable constant, the Conceptual Unit (www.CQthus.com/PT/CU), which is heuristically defined by the Elliptical Constant (www.CQthus.com/PT/EC); and which, can be rationalized as the radius of Infinity (www.CQthus.com/PT/ROI) (ROI).

I continue to make the point because no one seems to understand the significance of such a historic paradigm shift in understanding the environment and the unification of Science, Theology, and Philosophy (www.CQthus.com/PT/STP) (STP).

For over 50 years no world-clas s mathematicians has ever challenged or questioned my contentions/assertions.