Welcome to Aquarius, Volume 11 (10/16/2007): *The “Magic” Number MQ*

A) The “Magic” Number MQ (definition updated 12/28/2007)

B) Another, perhaps easier way to construct MQ and M

C) Is the core of *Proportion* found in the cosine/secant of 18 degrees?

A) The “Magic” Number MQ: The value of MQ is 1.000015321... .

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. *It is intended that the definition of MQ be corrected throughout the work presented here, especially in Volumes 8 through 14. However, the previous definition, imagined in error, may appear until revised.*

The proper definition of MQ is strictly the result of the construction steps described in *Values and Constructions Required*. The specific constructions that I claim are my original discovery are constructions #9 through #20.

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.

However, it is also true that IF the MQ constructed according to my discovery is exactly the same value as the MQ that is a factor in the product Phi^2, the factors being Pi * (5/6) * MQ, then the constructions I have discovered do in fact enable construction of **Pi exactly**.

The ancients knew there was this relationship among Pi, Phi and MQ and we did not know that MQ was constructible until July 7, 2007, the date on which I discovered with mathematical certainty that we can construct MQ to at least the 9th decimal place.

With reference to construction outlines B) and C) below: For detailed steps in these constructions, refer to Volume 8, and the Construction of MQ and M, and the main algorithm of constructing similar right triangles. Also the construction of the secant of 18 degrees and lines TN and NT.

B) __Another, perhaps easier way to construct MQ and M__:

(11/9)^2 * (cosine 18)^4 = 1.22215321234080739441649308240063...

(121/81) * (cosine 18)^4

= 1.49382716049382716049382716049383...

* 0.818135621484342140063933385739262...

= 1.22215321234080739441649308240063...

plus 11 = 12.2221532123408073944164930824006...

/ 10 = 1.22221532123408073944164930824006...

and we know this value, minus 0.2222, or plus 0.7778 minus 1

= 1.00001532123408073944164930824006... = MQ or M squared

and M = 1.00000766058769806778093094275226...

or M = 1.000007661...

C) __Is the core of Proportion found in the cosine/secant of 18 degrees?__

(secant 18)^4 * (81/121) [(81/121) = (9/11)^2]

1.22229123600033648574532213002996...

* (81/121) [0.66942148760330578512396694214876...]

= 0.818228017487828556573314814317575...

inverse = 1.22215321234080739441649308240063...

and 1.22229123600033648574532213002996... (secant 18)^4

/ by 1.22215321234080739441649308240063...

= 1.00011293482530290343440072984542...

= (TN)^2 or (1.00005646581845712470071810638815...)^2

__Notice, ancient manuscripts or hieroglyphs could have been misread__:

(6/5) = 1.2 (deemed an important value in ancient writings)

(11/9) = 1.222222222222222222222222222222...

(secant 18)^4 / (11/9) = TN = 1.00005646581845712470071810638815...

which is involved in the construction of MQ and Pi and squaring the circle,

as described in detail in Volume 8.

Back to (Welcome) or (Geometry Alpha Index) .