So I am asking for some help in parametrization of the helix shown in both attached diagrams (Where ever they may be marked. This is my first time posting attachments. Please look at them if you're interested). It is a coiled-coil and also, as you might better see from 002, the geodesics of a torus (only the torus is not standard).
Also, the expression of the "spiraling (logarithmic?) curve" is of interest to me. I want to find a connection between the two. I will explain why. But here's what I have.
I call this thing, a "contuatia". It is a circle of undefined radius, divided into twelve segments. The first line begins at the tenth division of the circle and descends and ascends across the circle, intersecting at the first division of the circle, with a value of e.
You might ask, how did I get such a value? Some people are able to estimate the value of certain things, simply by looking at them closely. e appears to my mind, as an absolute value -somewhere off in space. Hence, when I consider the value of e in my mind, I find that it falls exactly where I have indicated on the illustration. The same principle applies for the indication of the other numbers within the drawing as well. I'm simply able to imagine the locations of certain values. The drawing itself, was not a creative escapade. The lines appeared before me, just as the values on them did. Hence I simply drew what was all ready there. Poetic, n'est pas?
However, moving along. The second line leaves the tenth division of the first circle and approaches the apex of the circle, the twelfth division. Where the helix assumes its maximal outer value, there is an intersection between the twelfth division. The value of the helix at this point is 108. Here after it grows in value and intersects with the circle at every 30 degrees, only to terminate at the ninth division of the circle. This line, the second line, is a theoretical model of what may be the nature and formation of numbers, describing their distribution, in relation to the "first" line. I don't know, but...
Some things to consider. Where the first line equals 1, the second line equals 12. This is the primary relationship between the lines. Where the second line equals 36, the first equals 2. Hence a linear relationship is out of the equation. Obviously, from the drawing, that is the case. I'm not a genius, believe me.
Therefore the connection between line 1 and 2 is non-linear and, more importantly, can be understood by a simple description of the parameters which define each line. Notice also that where the first line equals (pi), one can draw a perfect circle, intersecting the value of 360 on the second line, the first division of the circle, and e, where it stands on the second line. If that's not worth calling mom, I don't know what possibly could be.
If the values on these illustrations seem too fascinating to be true, believe me, it is not because I have spent hours concocting this "contuatia", as I call it. As, I've already said, the lines appeared before me in my mind and I simply drew them. The values on each line were found by pure estimation.
Here's the basic value of this drawing. Where 12 and 1 connect on the second and the first line, the "distance" establishing their relationship is more or less linear. Where 36 and 2 connect, the relationship is becoming less linear. Notice, that everything important is in base 12 on the second line, and is something "else" on the first. The number 1, for instance. 2, e, pi, and so on -for the first. On the second, every intersect between the circle's bound and the maximal outer reach of the helix is a base 12 number. The growth is quite rapid. Termination at the ninth division might be the end of numbers as we know it. If you're curious what the spiral at the ninth to the middle is, I think it is a very rapid descent from a very HIGH number to zero, very rapidly. TOO rapidly, one might say.
e and 108 relate by the arc length formed by 30 degrees of the circle. And, finally, the last thing I can say is that where the first line equals (pi), the relationship it shares with the second is perfectly semi-circular. Hence, my interesting drawing.
I am not smart enough to put these lines into mathematical form. But if I could, I would be going nuts over this thing.
The lucky one will be the person who can paramaterize the first line, parameterize the second, describe the "distance" between the two and how it changes such that we get such interesting results between such interesting numbers on two such distinct curves. -finally, continue finding things within the patterned structure of the helix as it intersects the circle every 30 degrees (excepting the second loop, which occurs at 15 degrees).
The value of number line as it terminates at the ninth division represents the highest imaginable number. All other values are phantasms.