**Tini Circle Groups (TCG)**

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**This post is in memoriam: René Descartes**[1596-1650]

Tini is a neologism/acronym for

**T**angent,

*In**finity*

**I**nteger.

A Tini Circle Group (TCG) can begin with a circle that has a radius with a value of any Natural integer. The circles can diminish without end with radii of Natural integer (NI) curvatures. (Curvature is the reciprocal of the radius; i.e. One divided by the radius, "1/r.") The circles can be internally or externally tangent.

**Thus, it is hueristically illustrated that: there is never "space" that can be "empty."**

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Tini Cirt 1h with Tini Cirts: 2:1s, 3:1s, 4:1s, ad infinitum

Integer Curvatures from

One (The Elliptical Constant) to the Infinite

Tini Cirt 1h with Tini Cirts: 2:1s, 3:1s, 4:1s, ad infinitum

Integer Curvatures from

One (The Elliptical Constant) to the Infinite

Integer values

for the letters A thru G, above,

can be generated by

*any*Natural integer.

All circular curvatures (reciprocal of the radius) are Natural integers.

For every Natural integer, there is at least one, and often many arrays, that are all never ending. Can you calculate the Natural integer arrays and all their branches (corollaries)?

All curvatures are a simple algebraic function of the preceding array’s Natural integer curvature.

There are two categories of Tini Circle Groups (TCG): symmetrical and asymmetrical.

There are three types of asymmetrical Tini Circle Groups (TCG): single, dual, and hylotron.

All four of the various groups can be inserted within any circle of any other category or type of TCG.

All TCGs (of external circles) are uniquely described by the largest two circles of the group; and, when necessary, an alpha character designation is added for the type.

The term for uniquely defining a Tini Circle Group is Tini Cirt (Tangent Infinity Circle Term). An example of a Tini Cirt is: 8

**:**5a, which describes the large outer circle's integer curvature as 8; and the largest inner circle as 13 (8

**+**5); and, the category is asymmetrical..

All the following circles’ integers, to

*Infinity*

*,*are set by the first two circles’ curvatures; and, all integer circle curvatures are calculated with simple, algebraic arrays.

Of course, internal tangent circles are independent of the outer arrays.

Thus, internally and externally, every circle can have every space to

*Infinity*filled with a smaller circle that has an integer for its curvature.

One must ask: Why always Natural integers when the complex equation involves four variables to factor and square roots that must be divided?

Then, imagine that the symbolic packed circles are

spheroids in the manner of pulsing Pulsoids ...!

Why ?

And, again,

Why ?

And, again,

Why ?

Over and over,

until . . .

*Infinity.*

"Truth lies with simplicity,

which is Nature's signature."

"Truth lies with simplicity,

which is Nature's signature."

The basis of Tini Circle Groups is René Descartes' formula for Tangent Circles: See: Tangent Circles

©Copyright 2005-2008 by Brunardot. All rights reserved.

Terms: Dialogue21.com, Brunardot, and Pulsoid Theory must be cited.

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