The Mathematical Proposition Distilled
Welcome to Aquarius, Volume 14, Restatement of the Claim - History Treasure (January, 2008)
Based on a helpful observation made by a friend I have corrected the definition of MQ. I previously interpreted MQ as a variation of MQ+(1/MQ) = the integer 2 exactly. The true value of MQ+(1/MQ) is 2.000000000234... or 2 point followed by nine zeros, subject to greater accuracy that might be found with a high precision computer. The proper definition of MQ is strictly the result of the construction steps described in Values and Constructions Required.
Restatement of the Claim to Discovery
The Mathematical Proposition - a new calculation of Pi
With reference to the claim of discovery, upon review of the work presented here, the value MQ is defined only by the constructions described in Values and Constructions Required. The sum of MQ plus (1/MQ) is slightly greater than 2 exactly, being 2 followed by at least nine decimal zeros. The mathematical proposition, and physical proposition is based in part on the concept that physical Pi is variable and depends on the number of sides of a regular polygon, and on the concept that infinite Pi does not exist in the real physical universe. Therefore, construction of MQ enables construction of Pi to the ninth decimal place, which is a precisely accurate value for physical Pi when a regular polygon has 262,144 sides. The SF solution presented here I therefore claim is the best solution proposed to be the solution sought from a Pythagorean student, or candidate, in response to the original riddle. The geometry and understanding of Proportion practiced by the Pythagoreans is the equivalent of modern fractal geometry and chaos theory, and is the origin of shapes and structures, and is in effect the origin of evolution. Evolution is the origin of species and Proportion is the origin of the self-organization of matter.
I restate my claim that my work presents the valid solution, or certainly the best solution to date of the historical riddle,meaning that my work shows there was and still is a meaningful positive geometric answer to the original geometric riddle. And the solution I have discovered or re-discovered is suitable as the achievement in geometric constructions that the Pythagoreans would recognize as the indicator that the student has risen to the level of skill of a Master Geometer or a Master Mason. The SF solution demonstrates a meaningful relationship between Pi and Phi. The SF solution grows out of the process of following the clues embodied in the Great Pyramid and Pythagorean constructions.
Phi^2 = Pi * (5/6) * MQ, this MQ being the MQ constructed as described in Values and Constructions Required, and that this value for Pi is a correct value for the variable of physical Pi, to the 9th decimal place. I claim that in the real physical world, there is no physical object that can or does possess the proportional or circular dimension of infinite Pi, and that the closest any real physical object can come to being a Euclidean circle or sphere is to possess the proportional dimensions of a many-sided regular polygon. I believe that the atom is a polygon.
As illustrated by the following computer calculated output, 2 times pi to the 9th decimal place is the perimeter/circumference of a potential circle or regular polygon with 262,144 sides.
physpi01.cpp: Physical Pi in regular polygons, 01 (from prior to 2000)
Infinite pi = PE= CR = 6.28318530717958647692528676655901...
Index "6)" et cetera, is power to which 2 is raised:
6) With 64.00 sides, AR= 0.0981747704, SN= 0.098017140330
PE=(SD*SN)= 6.2730969811, /2= 3.1365484905 (3.1415926536)
7) With 128.00 sides, AR= 0.0490873852, SN= 0.049067674327
PE=(SD*SN)= 6.2806623139, /2= 3.1403311570 (3.1415926536)
8) With 256.00 sides, AR= 0.0245436926, SN= 0.024541228523
PE=(SD*SN)= 6.2825545019, /2= 3.1412772509 (3.1415926536)
9) With 512.00 sides, AR= 0.0122718463, SN= 0.012271538286
PE=(SD*SN)= 6.2830276023, /2= 3.1415138011 (3.1415926536)
10) With 1,024.00 sides, AR= 0.0061359232, SN= 0.006135884649
PE=(SD*SN)= 6.2831458807, /2= 3.1415729404 (3.1415926536)
11) With 2,048.00 sides, AR= 0.0030679616, SN= 0.003067956763
PE=(SD*SN)= 6.2831754506, /2= 3.1415877253 (3.1415926536)
12) With 4,096.00 sides, AR= 0.0015339808, SN= 0.001533980186
PE=(SD*SN)= 6.2831828430, /2= 3.1415914215 (3.1415926536)
13) With 8,192.00 sides, AR= 0.0007669904, SN= 0.000766990319
PE=(SD*SN)= 6.2831846911, /2= 3.1415923456 (3.1415926536)
14) With 16,384.00 sides, AR= 0.0003834952, SN= 0.000383495188
PE=(SD*SN)= 6.2831851532, /2= 3.1415925766 (3.1415926536)
15) With 32,768.00 sides, AR= 0.0001917476, SN= 0.000191747597
PE=(SD*SN)= 6.2831852687, /2= 3.1415926343 (3.1415926536)
16) With 65,536.00 sides, AR= 0.0000958738, SN= 0.000095873799
PE=(SD*SN)= 6.2831852976, /2= 3.1415926488 (3.1415926536)
17) With 131,072.00 sides, AR= 0.0000479369, SN= 0.000047936900
PE=(SD*SN)= 6.2831853048, /2= 3.1415926524 (3.1415926536)
**18) With 262,144.00 sides, AR= 0.0000239684, SN= 0.000023968450
PE=(SD*SN)= 6.2831853066, /2= 3.1415926533 (3.1415926536) **
19) With 524,288.00 sides, AR= 0.0000119842, SN= 0.000011984225
PE=(SD*SN)= 6.2831853070, /2= 3.1415926535 (3.1415926536)
20) With 1,048,576.00 sides, AR= 0.0000059921, SN= 0.000005992112
PE=(SD*SN)= 6.2831853071, /2= 3.1415926536 (3.1415926536)
Examination of the constructions in Values and Constructions Required takes time. Possibly no mathematician will take the time to do this. Possibly no historian will take the time to do this. But I have satisfied myself that the content of the knowledge of the ancient Pythagoreans was comparable to modern fractal geometry and chaos theory. They understood that physical Pi is variable and Proportion is the number system of Nature and Proportion is the sufficient cause of the self-organization of matter, the origin of life in the universe. They knew that it is possible, as described here, to construct Pi to the 9th decimal place using only a compass and straightedge. They left us a trail of clues, including the pentagon, Phi, the pentangle and 11/9ths or 1.222222222..., which was misinterpreted previously as 6/5ths or 1.2. Please review Squaring the Circle Exactly for more details about the trail of clues.
Hereafter, Welcome to Aquarius is likely to focus on the importance of stewardship, and let squaring the circle in Volumes 1-15 be like an old recipe that cooks can try if they wish. I believe it is possible for a physicist to deem credible the proposition that physical Pi is variable but it is not likely that mathematicians will be able to let go of infinite Pi. Infinite Pi lends an air of warm mysticism that mathematicians want to believe in to temper the otherwise cold mechanism of mathematical calculation. Mathematicians constantly try to persuade the general public that mathematics is imaginative. I believe that mathematics is the very least imaginative of all human neurological capacities. Mathematics succeeds only if it is physically accurate. Mathematics is counting and measurement. When counting and measuring the imagination must be disengaged and direct observation of physical reality must prevail. Imagination is a tool of science but not of mathematics. Imagination is useful for seeking knowledge, but once proper knowledge is found, it is no longer imagined and it is cannot be changed by imagination.
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