Text: After using the Quantize program for a short time, one will notice that some of the roots have a series that begin and end with even numbers, and the two center ones, e and d, are odd. This points up something which was thought trivial about the Prime Pythagorean triangles, but appears to be quite important. These even valued roots inject a concept of "doubling" or the influence of "2". The ellipse which these roots project, is turned on end, that is, the ellipse is rotated through ninety degrees, when b > e, (vis; N > O), after doubling. The rotation of the ellipse is perhaps best demonstrated by reverting to the prime Pythagorean triangle from which the ellipse derives. In such a triangle, the sum and difference of the hypotenuse and altitude, G and F, is always a double square. At the same time the sum and difference of the hypotenuse and base, G, and C, are single squares. In the "doubling" process, the double of a single square is a double square, but the doubling of a double square is a single square. This, in effect, reverses the position of D and E, with A and B. Then such a triangle is considered to be rotated through ninety degrees. But the "doubling" process is not particularly a mathematical doubling. In fact it has nothing to do with doubling. In this doubling process the ellipticity of the ellipse is actually drastically changed. All ellipses fall on one side or the other of the basic ellipse which begins with the roots, 1, 1, 2, 3, which are in turn, representative of the 3, 4, 5, Prime Pythagorean triangle. When an ellipse or triangle have roots which are near to this value the doubling process causes little change. One side will have ellipses slightly more circular. The other side of this median will have ellipses slightly more elongated. If this "doubling" (see DOUBLING) concept has a reality and an application it would be in the case of the correlation between Earth orbit and the orbit of Halley's Comet. Note that the quantum numbers for them 1, 29, 30, 59, and 59, 1, 60, 61. This combination indicates that Halley's Comet has some special relationship with Earth. The "59" used as roots in both cases indicates a close synchronization between them, and the "1" in each case indicates a highly stabilized orbit, for each of them.

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