My advice would be to play a game with a real, in theory, and, actual, in practice, prize. You have to hit it only one time.

Originally Posted by

**1HitWonder**
BINGO!

2x^2 -2x + 102 = 0; 2x^2 -2x + 113 = 0. And, [102(1 + x^2) - 200x] / (1 - x)^3; [113(1 + x^2) - 222x] / (1 - x)^3.

Got the Fibonacci numeral, Phi, to go with the fine-structure inverse approximation 137 (with 411), and, next, going a bit further back the other way, the approximation 0.577, as in Euler's constant.

Ah, but how about a couple of little hints?

Firstly, the terms advance sequentially, on a circle of four axes, or eight parts, from the pair 106//113/113, to 117/114, to 126/125, to 137//142/162, to 186//153/173, to 197/214, to 246/225, to 257//282/322, for one complete turn, and, so on, as sums of pairs of squares. The leading numeral groups above switches between the two thus sequences, from the graphs of 2x^2 -2x + 102, and, 2x^2 -2x + 113.

Secondly, the term that connects the pair 106//113/113, to 117//102/102, which starts the other way around the circle, is 115//104/104 on the 106//113/113 side, and, 104//115/115 on the 117//102/102 side, of its part on one end of the circle, preferably at its bottom, with dimension-0 in spot-1 at its top. I think that there are eight different ways to properly construct the circles, together with a similar overall construction for the other, alternate universe. However, it helps to have a bit of numerical talent, feel, and/or experience. Say, to deduce at least that the index of 137 is 3*137 =411; to go with that of 142, which is 2*142 = 284 = (300 -16) ---> 316, as 3.16 is the start of √10.

Next, one may easily examine the curiously coincidental results of the various thus numerals, by their factorization, sums/differences, and so on. Furthermore, thus even mathematically calculate the electromagnetic fine-structure constant, which they say can't be done - even though a string of famous physicists, and others, still try. The other day, I arrived at alpha = about 1 / 137.035999094478 ... , to an arbitrary number of digits. The other one, 1 / 142.736000895392 ... , was a bit harder to figure, because there was no preexisting approximation to go by, but, ultimately, both had to be simultaneously worked out the remainder of way.

https://en.wikipedia.org/wiki/Fine-structure_constant
The idea was to take the in-between case of the two extremes to do with every thing working out exactly, the latter which involves the determination of the exact sums/differences, and the exact products, of the two different electromagnetic fine-structure constants. For a third hint, (137 + 142) = 297 is an exact sum, whereas ([1][3^2].[7] * 14.2) = (19.7 * 14.2) = 279.74 is an exact product; as opposed to the sort and degree of exactness of determining where the two thus constants have their sum as product. The latter is where the resultant digits of the two thus constants progress in essentially random fashion. The case in between turned out to be fairly straightforward despite the stunning presentation of the ordering of their digits, once I realized what the heck was going on overall with the two thus constants. Would have been a lot harder though without a good portion of the start of the electromagnetic fine-structure constant for our universe.

Actually, I did spend a couple of days to work out the thus constants for also the alternate pair of universes. The complete set of denominators are: 137.035999094478 ... with142.736000895392 ... , and, 89.266558436785 ... with 62.712232300788 ... . These weren't so hard to figure, going more by the format of the other thus calculations, and a couple of other tricks, than by the exact extremes method. Turned out that there were limited thus possibilities. Thankfully.

Well, years ago, I did mention the possibility of putting up my very own theory of everything, in this very forum, but, as circumstance would have it, it came down to a very few thus numerical observations. But, not to conclude that there really, and actually, isn't so much more to it all. And, I could go into a lot more detail with even the thus numerals, but, it's a delicate balance, at this point, to put it out there only to the point of proving, later on, that it existed. Would love to elaborate, and on the odds against the numerals randomly turning out, freaking unbelievable, but, thankfully, no one here could gainfully explore with it, anyway, and, I don't think that anyone much trusts even Dan Druff, anymore, who, like almost everyone else on the forums, became just another gambling world casualty of life. Not exactly the stuff of significant lasting value, truly great, for the ages. Not exactly "cool", either. Only a handful of never-weres gave a crap about the casino stuff. Such persons looking for any sort and degree of a win, let alone in front of an audience of their peers. The reasom that they, just, can't put it down. Why care at all about such claims whether true? Sorry, but such is hardly entertainment, either, but, at best, a strange, voyeuristic waste of a heck of a lot of time.

Post #3844 = 62^2 . For someone who very recently turned 62. Ha.

P.S. Had a little bit of time to try to work out, aka "decode", pi in terms of working out the numerals above. Not extremely surprising that it worked out, in the same way as the others, if it was going to thus work out, because pi is part of the physics calculation of the electromagnetic fine-structure constant. I would love to post such calculations, but, at this point, I've already written enough about it here. Probably will hit the headlines, once published, after some relaxation, a few more tests, a few other matters to attend, and, whatever else comes up until then.

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