Tini Circle Groups

[Epsilon=One]

Tini Circle Groups (TCG)

Tini is a neologism/acronym for Tangent, Infinity Integer.

Tini Circle Groups (TCG) can begin with a circle that has a diameter with a value of any Natural integer (www.101123.com/NI). The circles can diminish without end with diameters of Natural integer (NI) curvatures. (Curvature is the reciprocal of the diameter; i.e. One divided by the diameter, "1/d.") The circles can be internally or externally tangent.

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

(If no image appears below, "Click" your browser "Refresh" icon.)
http://www.2-CQ.com/PT/TiniCirs/8-5l.gif
http://www.2-CQ.com/PT/TiniCirs/84-72l.gif
http://www.2-CQ.com/PT/TiniCirs/231-147l.gif
http://www.2-CQ.com/PT/TiniCirs/381-254l.gif
http://www.2-CQ.com/PT/TiniCirs/1-1l.gif
Integer values
for the letters A thru G, below,
can be generated by any Natural integer (www.101123.com/NI).
http://c.g2d.us/pulsl.gif

All circular curvatures (reciprocal of the diameter) are Natural integers (www.101123.com/NI).

For every Natural integer (www.101123.com/NI), there is at least one, and often many arrays, that are all never ending. Can you calculate the Natural integer (www.101123.com/NI) arrays and all their branches (corollaries)?

All curvatures are a simple algebraic function of the preceding array’s Natural integer (www.101123.com/NI) 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 (www.101123.com/I), 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 (www.101123.com/NI) when the complex equation (www.101123.com/TC) involves four variables to factor and square roots that must be divided?

And also ask: from which direction (or source), the circumference or the center, are the tangent Infinity circles generated?

Why ?
And, again,
Why ?
And, again,
Why ?
Over and over,
until . . . Infinity.
For formulas of Tini Circle Groups' Tangent Circles see: Tangent Circles (www.101123.com/TC)

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[Epsilon=One]

I remember being wrecked when I read in Sci. Am. about inverse radius, or curvature, solving these things. OK, I like it! (This should maybe be moved to TINI Circle Groups.)It's moved.

I've worked out the arithmetic for arrays beginning with any integer curvature and progressing to infinite curvature for all space.

This is why I contend there is no "empty" space in the Universe. And, why I prefer the neologism: Dyosphere (http://www.physicsmathforums.com/showthread.php?t=151).

As you look at a circle group, imagine the circles are bubbles that are expanding as they slow down.

The bubbles move at the SOL and slow to motionlessness where they are again points and the process repeats.

It is not a question of does this occur; but, it's a question of: Why is the geometry as it is? Specifically: Why integers??? Remember, Nature defines mathematics; not vice versa.

Heuristically, this is what is going on with the background quanta that I refer to as Pulsoids (http://www.physicsmathforums.com/showthread.php?t=98).

[ste]

What practical use do these circles have? How can they help us understand Reality? Why should their grouping in this fashion be of interest? What is the significance of the circles chosen? What is the significance of each array? Why are Natural Integers used? Why are they grouped in the fashion which they are?

The bubbles move at the SOL and slow to motionlessness where they are again points and the process repeats.What prompts this action? How is it maintained?

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

And also ask: from which direction (or source), the circ umference or the center, are the tangent Infinity circles generated?

I hereby ask those questions right now.

[Epsilon=One]

What practical use do these circles have?What applications do most mathematical manipulations have? However, in the case of Tini Circle Groups, they heuristically describe the manner that Emergent Ellipsoids (www.EmergentEllipse.com) (Spheres/circles are special ellipsoids/ellipses) fill all “space.”

How can they help us understand Reality?They, heuristically, demonstrate the manner that all quanta emerge, fill the Universe, and dissipate.

Why should their grouping in this fashion be of interest?The geometry/Unimetry (www.CQthus.com/PT/Unimetry) is one of the most important concepts that explains what is inexplicable in conventional theoretical physics.

What is the significance of the circles chosen? What is the significance of each array?They demonstrate that any circle can begin the algorithm/matrix and they demonstrate all the different categories. The curvatures are endless within every opening. Thus, a close relationship to the infinite and the infinitesimal.

What is the significance of each array? Why are Natural Integers used?Because Nature doesn’t recognize partial “charges” (despite Murray Gell-Mann’s erroneous quark theories). The curvatures are symbolic of double vectors which harmonize and resonate.

Why are they grouped in the fashion which they are?Vectors are quaquaversal (all possible directions); but, only such a grouping, as the Tini Circle Groups, harmonizes and resonates to quanta.

What prompts this action?Seminal motion (www.CQthus.com/PT/SM) from the chaos of the singularity.

How is it maintained?All phenomena that emanates evolves and dissipates to emanate again.

One must ask: Why always Natural integers when the complex equation involves four variables to factor and square roots that must be divided?This is the elegance and beauty of all the mathematics of Unimetry (www.CQthus.com/PT/Unimetry) that more than anything else makes Pulsoid Theory (www.CQthus.com/PT/PTis) near irrefutable.

And also ask: from which direction (or source), the circ umference or the center, are the tangent Infinity circles generated?They are heuristic. However, quanta, within Reality (www.CQthus.com/PT/R) begin at near infinite speed and infinitesimal size and dissipate to near infinitesimal speed and infinite size, while they endlessly cycle.

I hereby ask those questions right now.And, I hereby answer “those questions right now.”