The Lemma Ellipse

[Epsilon=One]

Lemma Ellipse

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http://www.2-CQ.com/PT/Ellipses/let500.gif
The Lemma Ellipse is an Ultron Ellipse (http://www.physicsmathforums.com/showthread.php?t=183) that has a Natural integer (http://www.physicsmathforums.com/showthread.php?t=100) value for the lemma, "l" (Line BK).

..........Legend for a Lemma Ellipse

Line AB = FK = hypotenuse = h
Line AD = BJ = radius = r
Line AJ = diagonal = D
Line BC = CD = soliton = s
Line BD = wave = w
Line BF = vector = v
Line BG = ED = apogee = o
Line BK = lemma = l
Line CA = CJ = diagonal radial = d
Line CF = CH = amplitude = a
Line CG = EC major radial = m
Line DG = EB = perigee = p
Line EG = major diameter = M
Line FH = minor diameter = A
Line GH = diameter chord = c
Line oP = Hypotenuse radius = Hr = Natural integer (http://www.physicsmathforums.com/showthread.php?t=100)
Line oV = Vector radius = Vr = Natural integer (http://www.physicsmathforums.com/showthread.php?t=100)
Line oR = Radial diameter = Rd = Natural integer (http://www.physicsmathforums.com/showthread.php?t=100)
Line oT = Chord diameter = Cd = Natural integer (http://www.physicsmathforums.com/showthread.php?t=100)
Line oL = Lemma diameter = Ld = Natural integer (http://www.physicsmathforums.com/showthread.php?t=100)
Triangle ABD = Hypotenuse triangle = Brunardot triangle (http://www.physicsmathforums.com/showthread.php?t=255)
Triangle BCF = Vector triangle = Pythagorean triangle
Triangle BCJ = Radial triangle = Pythagorean triangle
Triangle BFK = Lemma triangle = Pythagorean triangle
Triangle CGH = Chord triangle = Pythagorean triangle
Inscribed circle ABD = Hypotenuse circle
Inscribed circle BCF = Vector circle
Inscribed circle BCJ = Radial circle
Inscribed circle BFK = Lemma circle
Inscribed circle CGH = Chord circle

p, s, v, o = first four terms of a Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99)

All lines shown in the above image are integers derived from simple algebraic relationships for an unending sequence of Lemma Ellipses that are generated from two unending sequences of Natural Integers (http://www.physicsmathforums.com/showthread.php?t=100).

The Lemma Ellipse is associated, heuristically, with internal bonding of fundamental and evolved physical manifestations

Lemma Ellipses are generated by any two Time/Cycle integers that are combinations of factors in groups referred to as Lemma factor groups.

There are 40 Lemma factor groups that give Time/Cycle values that are between 759 and 1,830, which are:

| 3x11x23 | 2x2x5x53 ! 23x47 ! 2x11x59 ! 3x463 ! 2x3x5x47 !
| 2x2x3x7x17 ! 2x733 ! 1483 ! 5x3x101 ! 5x5x61 | 29x53 |
| 2x2x5x7x11 | 2x2x2x193 | 1579 | 2x2x3x7x19 | 2x17x47 | 1601 |
| 2x3x3x89 | 1627 | 31x53 | 1663 ! 3x557 | 2x839 |
| 2x2x421 | 2x2x5x5x17 | 3x571 | 3x5x5x23 | 2x5x173 | 2x3x17x17 |
| 37x47 | 2x3x3x97 | 2x881 | 2x2x443 | 1777 | 3x593 |
| 2x3x13x23 | 2x17x53 | 2x2x2x2x113 | 2x3x5x61 |.
After the last Lemma factor group | 2x3x5x61 |, any group of factors that produces a Time/Cycle integer larger than 1,830 will generate a Lemma Ellipse (LE).

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