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Extract No.26
Ancient
Pi ():

360 / 114.285714  =  3.150000008  (pi proportion for 360c circle) 
260 / 114.285714  =  2.275000006  (pi proportion for 260c circle) 
Note that the 3.15 number offers a mediatio/duplatio series
based on the 63c, which was significant in ancient reckoning systems:
315, 630, 1260, 2520, 5040, 10080, 20160, 40320, 80640, 161280, 322560,
645120,1290240, 2580480 (a Precession number/fractal); and, 63,
126, 189, 252, 315, 378, 441, 504, 567 (kemi), 630, 693 (Sothic), 756 (Giza), 819 (k'awil; maya), 882, 945, 1008,
1071, 1134 (Nineveh, 2 x 1134 = 2268), 1197, etc.
Note that the 2275 fractal number is relevant for the computational
series within the ancient reckoning system of the 364c daycount:
2275, 4550, 9100, 18200, 36400, etc. Also, note that the difference
between the Nineveh 2268c and the pilike number 2275 is seven (2275 
2268 = 7); which could be easily translated from one series to the other
by remainder math based on multiples of seven.
Many of the distinctive historically significant numbers of the ancient
reckoning system reflect a relationship based on the reciprocal of seven.
Consider the maya long count period number of 1872000, which
has received so much speculation regarding its beginning and ending date.
Also, consider the period called the k'awil of the maya cited as
consisting of 819c days. Now, notice the number that obtains from
the division resulting from half of the long count period figure by the
k'awil: 936 / 819 = 1.142857143. The same figure obtains
regarding the constant length of a diameter of a circle based on a pilike
number in relation to the reciprocal of seven as explained earlier.
Other relationships obtain regarding similar historically significant
numbers from other systems. The Great Pyramid entails the number 756c
as its baseline. Also, there exists the 432c number/fractal associated
with the Consecration. If we double the 432 figure and divide by the 756c,
the same result obtains: 864 / 756 = 1.142857143. Consider: 360
x .864 = 311.04 (31104 being an historically significant number for China
and Mesoamerica).
The significance of seven and its reciprocal becomes obvious throughout
the historically significant numbers/fractals. Even the obvious relationship,
of the 364c daycount of ancient Mesoamerica, which was employed for computations,
reveals a direct basis of seven: 364 / 7 = 52. Immediately, one
will recognize the 52c that is so wellknown in ancient Mesoamerica as
the calendar round (52 years times 365 days = 18980 days; and 52 years
times 360 days = 18720! days). And, the ancient kemi appear to have employed
a 54c in its place: 7 times 54 = 378 (2 x 378 = 756; or, 7 x 108
= 756). No matter where one turns, the number seven and its reciprocal
make their appearance. The reasoning behind this procedure may be rather
obvious, although we have not discerned it previously.
The number 1.142857143 concerns the ratio 8/7ths. The Aztec Calendar appears
to be based upon a spatial division that reflects the logic of 7:8 or
8:7, depending upon the rings and segments to be considered (Cfr., Earth/matriX
No.88). If one were attempting to consider the diameter of the Solar
System, or the Universe, knowing that these events consist of imaginary
circles (ellipses), then the use of the unit 1.0 for the length of their
respective diameters would not be of much value. And, furthermore, if
the ancients had employed the contemporary (and possibly past) concept
of pi (based on a close approximation to 3.141592654, give or take a fraction),
then the numbers would have been unmanageable and not very attractive.
The apparent relational aspects of the many different historical numbers
found in the many distinctive ancient reckoning systems suggest a common
origin and reasoning. If the length of the diameter of the solar system
or the Universe were assigned a value consisting of the reciprocal of
seven (i.e., 1.142857143), then this would be the next best thing to working
with whole numbers for computing the time cycles of the movement of the
planetary bodies and the stars. Furthermore, knowing the actual measurement
of pi (the exact proportion of the diameter:circumference ratio) could
be compensated with remainder math adjustments quite easily. Consider
the following computations:
1.142857  x  819  =  935.999883  (936)  (maya long count fractal) 
1.285714  x  819  =  1052.999766  (1053)  
1.428571  x  819  =  1169.999649  (1170)  (Venus sidereal count) 
1.571428  x  819  =  1286.999532  (1287)  
1.714285  x  819  =  1403.999415  (1404)  (kemi count; 351c) 
1.857142  x  819  =  1520.000298  (1521)  (39²) 
1.142857  x  315  =  359.999955  (360)  (360c; kemi; maya) 
1.285714  x  315  =  404.99991  (405)  (1296000c; kemi) 
1.428571  x  315  =  449.999865  (450)  (maya long count; 9 base system) 
1.571428  x  315  =  494.99982  (495)  (99c lunar count) 
1.714285  x  315  =  539.999775  (540)  (kemi count) 
1.857142  x  315  =  584.99973  (585)  (Venus synodic count) 
1.142857  x  2268  =  2591.999676  (2592)  (Platonic Year, 25920 years) 
Scholars consider the figure of 3 1/7ths to
have been an erroneous computation for pi. Yet, we have never really known
how the ancients computed their mathematics. The few documents that remain
(such as the Rhind document of the ancient kemi) concern everyday matters;
not the mathematics and geometry of the study of the Universe. By employing
the reciprocal of seven in the computations, which is what an initial
analysis of the historically significant numbers reveals, the ancients
may have been seeking an easier method for arriving at their knowledge
of the Universe than what is offered by the precise unending fractional
expression of pi, the proportion of the diameter to the circumference
of a circle. This may be further understood when we realize that the comings
and goings of the planetary bodies and the stars throughout the Universe
do not travel on perfect pilike circles.
The ancients may have employed distinct constant fractals/numbers for
adjustments in their computations: the length of the diameter may
have been based on 114.2857, 114.591559, 114.638448; etc; the distance
of the circumference may have been related to the 260c, 360c, 378c,
936c, etc.; and, the pi ratio (proportion) of the diameter:circumference may have been 2.268, 3.15, 3.1416, 3.142857, 819, etc. The distinctive
historically significant numbers reflect different aspects of the computations
and their corresponding adjustments. From this dynamic perspective, the
historically significant numbers may be communicating to us a much more
precise knowledge of astronomy and mathematical and geometrical computations
than we have been willing to concede to the ancients.
email: Charles W. Johnson
©19982013 Copyrighted by Charles William Johnson. All rights reserved.
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Links:
Ancient Phi and Its Extension
The Concept of Pi and the Ancient
Reckoning Numbers (Trigono/metriX)
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