 Charles William Johnson Mathematical and Geometrical Minutiae Index
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Charles William Johnson Mathematical and Geometrical Minutiae Index
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1. The Maya Companion Number: 1385540
| 1.38554 |
 |
LOG 10x | = | .141619068 | |
| 13.8554 |
|
LOG 10x | = | 1.141619068 | |
| 138.554 |
|
LOG 10x | = | 2.14169068 | |
| 1385.54 |
|
LOG 10x | = | 3.14169068 | (pi-like figure) |
| 13855.4 |
|
LOG 10x | = | 4.14169068 | |
| 138554 |
|
LOG 10x | = | 5.14169068 | |
| 1385440 |
|
LOG 10x | = | 6.14169068 |
2. The Precession Figures: 94965000 days
The ancient Calendar Round of Mesoamerica consists of 18980 days. Half of that figure is 9490 days.
The Great Cycle of the Precession may be considered to be:
| 26000 years | x | 365 | days equals | 9490000 | days | |
| 26000 times | x | 365.25 | days equals | 9496500 | days | |
| 25920 times | x | 365 | days equals | 9460800 | days | [maya fractal 4608] |
| 25920 times | x | 360 | days equals | 9331200 | days | |
| 25956 times | x | 360 | days equals | 9344160 | days | [the maya count] |
There are many options in this respect. Consider the computational possibility regarding the concept of pi and the precession figure or calendar round figure:
| 9490 / p (3.141592654) | = | 3020.76082 | [fractal; floating decimal place] |
| 1510.38041 | |||
| 755.190205 | [Great Pyramid: 756c] |
{Note.- The baseline of the Great Pyramid has been frequently cited to be 756c feet (times four sides = 3024).
3024
1512
756
378
189
represent, then, historically significant Kemi counts. One must remember that Pakal, the Great Maya King at Palenque, was found to have a jade tube necklace with 189 beads.}
Various adjustments in the previous measurements cited become available.
For example, consider,
| 365.256 | x |
26000
|
= | 9496656 [relation to 1366560 maya companion] | |||
|
9496656 - 136656
|
= | 9360000 | [maya period] | ||||
| 9496656 | / |
Pi; (3.141592654)
|
= |
3022.879491
|
[fractal] | ||
|
1511.439745
|
|||||||
|
755.7198726
|
[Great Pyramid] | ||||||
3. The Anti-Radian and the Precession
We have called the figure 114.591559 the diametian, simply meaning two radians.
| 360 / pi = | 114.591559 |
| 57.29577951 [the Radian] |
The anti-Radian is the remainder of the circle once the Radian is subtracted thereof:
360 - 57.29577951 equals the Anti-Radian, 302.7042205
The Precession figure divided by pi yields an Anti-Radian like number:
9496500 / pi = 302.2829834c fractal [Adjustments may be obtained.]
4. The Anti-Radian and Pi
Pi to the seventh power:
| 3.1415926547 | = | 3020.293228 [fractal; Anti-Radian = 302.7042205] |
| 3.1428571427 | = | 3028.813169 |
| 755.7909764 x 4 | = | 3023.163906 the seventh root of which is 3.142019047 (pi-like number). |
5. The Sothic Cycle Number: 1649.457812
Consider the Sothic Cycle number, which we have perceived to exist encoded within the Sothic Calendar as 1649.457812457812457812, and how it relates to the concept of pi and the Great Cycle of the precession (25920 years).
The reciprocal of pi as an expression of the reciprocal of seven is:
Pi as the reciprocal of seven = 3.142857
| 1 / 3.142857 | = | .318181833 |
| 1649.457812 / .318181833 | = | 5184.010025 |
| [25920c Great Cycle] |
6. The Sothic 1649.47812 and Its Counts In Opposition
| 1649.457812 / 3 | = | 549.819270666 |
| 549 - 819 = 270 |
The Sothic count displays an encoded symbolism from the start. Now, consider the opposite counts of these particular counts encoded into the 549.819270666 number:
| 900 - 549 = 351c | [kemi] |
| 900 - 819 = 81c | [kemi and maya] |
| 900 - 270 = 630c | [kemi] |
| 900 - 666 = 234c | [maya: 234, 468, 936, 1872c] |
Further, consider the sum of the opposite counts:
351 + 81 + 630 + 234 = 1296c [kemi and maya --nine baktuns fractal]
549 + 819 + 270 + 666 = 2304c [maya alautun]
It should come as no surprise that these two sums reflect the ancient reckoning count of both the maya and the kemi systems:
2304 + 1296 = 3600c
Or, consider further: two kawils (819c), i.e., 1638c minus one alautun, 2304 equals 666c
Some historically significant counts:
|
Kemi
|
Maya & Kemi
|
Kemi
|
Maya
|
|
351
|
81
|
630
|
234
|
|
549
|
819
|
270
|
666
|
|
Sothic
|
Maya
|
Kemi
|
Bible
|
Computations based upon the ancient, historically significant counts arise in a natural flowing manner:
1404 x 549 = 770796
1405 which reminds us of the 7776c, 3888c historically significant count of Meso-America.
770796 - 7776 = 693036c yielding intriguing combinations of counts.
7. The 900c as the Baseline count
If the 9, 90, 900 fractal expression is historically significant, then let us examine the counts in opposition to the Sothic number 549.819270666, as viewed above partially.
|
819
|
1089
|
540
|
1036
|
||
| (90c difference) | |||||
|
729
|
999
|
450
|
846
|
||
| (90c difference) | |||||
|
639
|
909
|
360
|
756
|
||
| (90c difference) | |||||
|
549
|
819
|
270
|
666
|
= Sothic Baseline Counts | |
| (90c difference) | |||||
|
459
|
729
|
180
|
576
|
[constant factor; Jim Branson] | |
| (90c difference) | |||||
|
369
|
639
|
90
|
486
|
||
| (90c difference) | |||||
|
279
|
549
|
0
|
396
|
8. The Sothic 1649.47812 and the Maya 1385540
| 1649.457812 / 693c (Sothic) | = | 2.380170003 / 2 |
|
...
|
||
|
1.385441284 -10
|
9. Proportionality within the Ancient Reckoning Counts
From the previous computations, one may derive a general system of reckoning based upon the proportionality of the historically significant counts. Consider the counts in opposition in the same manner as a difference of 90c.
| 621 | 351 | 900 | 504 | |
| (90c difference) | ||||
| 531 | 261 | 810 | 414 | |
| (90c difference) | ||||
| 441 | 171 | 720 | 324 | |
| (90c difference) | ||||
| 351 | 81 | 630 | 234 | |
| (90c difference) | ||||
| 261 | -9 | 540 | 144 | |
| (90c difference) | ||||
| 171 | -99 | 450 | 54 |
From these counts, combinations of the historically significant counts become available in an infinite relation of proportion.
| 171 + 909 | = | 1260 |
| 1089 + 351 | = | 1440 |
| 819 + 621 | = | 1440 |
| 729 + 531 | = | 1260 |
| 819 + 396 | = | 1215 [Hydrogen spectra; Jim Branson] |
| Etc. |
10. The Kemi 756c and the Maya 576c
| 7562 | = | 571546 |
5762
|
= | 331776 |
| 756 x 576 | = | 435456 | |||
| 756 / 576 | = | 1.3125 |
576 / 756
|
= | .7619047619 |
| 435456 x 1.3125 | = | 571536 | (7562) | ||
| 435456 x .7619047619 | = | 331776 | (5762) |
11. Quasi Pythagoran Theorem in Numerical Symbolism: 666c
|
576 x 360
|
plus
|
756 x 360
|
= |
666 x 720
|
|
207360
|
plus
|
272160
|
= |
479520
|
The 666c functions as a number constant between the two ancient reckoning systems of the Maya (576c) and the Kemi (756c).
Both of the ancient reckoning systems of the Maya and the Kemi employed a 360c. The Maya employed a calendrical 260c, although it is not known whether the ancient Kemi employed the 260c dy-count. However, the computations would tend to confirm such a possibility.
| 576 x 260 = 149760 |
756 x 260 = 196560
|
One must note immediately that:
196560 - 1366560 = 1170000 [Venus count 117c]
Now, 196560 plus 149760 = 346320 / 666 = 520
Remember, the 52c is the Meso-American Calendar Round of 52 years times 365 days = 18980 days, or, one calendar round.
Further consider: 196560 / 346320 = .567567567 [Nineveh count 567c]
567 x 4 = 2268c [Nineveh count]
149760 / 346320 = .432432432 [the Consecration]
576 : .432432432 : 666c756 : .567567567 : 666c
[Note.- 819 x 693 = 567567]
The relationship of proportion [ 567 : 432] functions as reciprocal factors as of the 576, 666 and 756 counts. All of these counts function in this manner as of the ancient 260c (or 520c) count. One may thus entertain the possibility that the ancient Kemi reckoning system was designed as of the 260c ancient reckoning system of ancient Meso-America. At least, the ancient Kemi numbers function in harmony with the 260c system.
The additional conclusion is to consider the possibility that the ancient Nineveh system also employed the 260c. A more far-reaching conclusion would be to consider the possibility that all of the ancient, reckoning systems were one and the same. The ease of computation and translation between one system or another flows effortlessly from all of the ancient reckoning counts, as we have been seeing throughout the Earth/matriX series of essays.
In fact, one may even visualize the baseline of the Great Pyramid as a function of the 666c and the Nineveh count (1134c):
1.134 x 666 = 755.244
By the way, one cannot help but recall the music of India in this regard, with one of the basic scales based on the sequence: 4324432. Other similar scales of ancient India are: 4342432 and 4333432.
756 x 576 = 435456 - 432432 = 3024
12. The 666c in Relation to the 693c and 936c Counts
| 693c – 666 = 27 |
936c - 666 = 270
|
The Kemi 540c (270c) makes its appearance in relation to the Sothic 693c and to the Maya 936c (1872c).
It is not surprising, then, to find numerous relationships through addition and subtraction of the 666c and the ancient reckoning counts.
|
666 - 378c (Kemi)
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= | 288c (Maya) |
|
819 (kawil) - 666
|
= | 153c |
|
1296 - 666
|
= | 630 |
13. The Sothic 549.819270666
| 549.819270666 / 666 | = | .82555446045 |
| 1.6511089209 |
1.6511089209 minus Sothic 1.649457812 = .00165110845 same difference
14. The Speed of Light and Some Ancient Reckoning Counts
432 : 567 : 576 : 666 : 756 when these five ancient reckoning counts are added together, we obtain the sum: 2997c
The speed of light is given today as fractal 2.99792458
15. The Three Sixes
In the Bible, the number of the Beast is given as 666c.
756 + 576 = 1332
378 + 288 = 666
One may understand a reading of "three sixes", meaning 3•6, or three-sixes, as in the 36c count. One might consider such a reading as in opposition to the ancient 360c counts of those cultures in opposition.
One cannot help but note that the square root of 666c is extremely close to today’s figure given for the Precession:
666 = 25.8069758
[fractal for 25800 years]
Further: 258002 = 665640000 [remember 1366560c maya companion]
16. Hydrogen and the Reciprocal of Seven as Pi
|
1 / 3.142857142
|
= | .318181818 | |
|
3.168 x .318181818
|
= | 1.0079999942 | [Hydrogen 1.00794 atomic weight] |
Now, remember, the historically significant number, 3168 also relates to the 2592c Great Cycle number by way of the maya long count:
3168 - 2592 = 576 [57600000 calbatun]
Then, one might consider the 3168c figure to relate to the height of the Great Pyramid, which has been cited to be around 481.5 fet high.
| 3168 | ||
|
+
|
1649.457812 | |
| 4817.457812 | [fractal] |
17. The Legend of the Four Suns
One of the more commonly cited figures from the ancient codices, offered for the period of the Legend of the Four Suns in ancient Meso-America concerns that of 2028c years. A less frequently cited figure from another Codex concerns that of 2052c years.
756c (Kemi) plus 1296c (Kemi & Maya) equals 2052c [period of the 4 Suns]
18. The Enneagram Figure: 693c
The Enneagram number, 693c, is also found to be in abstentia within the Sothic Cycle number 1649.457812, since the 3, 6, 9 numbers are not contained therein. In this manner, they are encoded in a significant manner.
6932 = 480249 x 3 = 1440747
Now, 1440747 minus the kemi and maya number, 1296000, equals 144747:
| 1440747 | |
|
-
|
1296000 |
| 144747 |
Further consider:
| 6932 = 480249 x 3 = 1440747 minus 1404000 = | 36747 |
| 12249 | |
| 4083 | |
| 1361 | |
| 453.6666 |
The Nineveh number: 4536c as difference. All along the way of the computations one is constantl discovering relationships among various historically significant numbers and fractals as occurs with the maya long count 1404000 figure in relation to the 693c and th e Nineveh count of 4536c.
The 693c count is also known as that of Saros.
19 years x 365 = 693519. The Sothic 693c and the Kemi 963c
693 x 963 = 667359The Newtonian Constant of Gravitation is given today as fractal
6.67259
Therefore, a variant computation for the height of the Great Pyramid, based upon this fractal, would be:
| 667259 / 693 | = | 962.8556999 | |
| 481.4278499 | [481.5 feet Height Great Pyramid] |
20. Physical Minutiae
| Rydberg Constant fractal expression | 13.6057 |
| Boltzmann Constant fractal expression | 1.3807 |
| Maya Companion Number | 1366560 |
| Maya Companion Number | 1385540 |
21. Celestial Minutiae
100 lbs. Weight on Earth
254 lbs. Weight on Jupiter
Ratio of 2.54 (remembering conversion factor for inches to centimeters is 2.54 as well).
17 lbs. Weight on Earth’s Moon
|
254 / 17
|
= |
149.4117647
|
[Earth semimajor axis 149.6c 106 km]
|
|
1 / 17
|
= |
.058823529
|
[Jupiter distance from Earth 588.5 106 km]
|
Subtract the semimajor axes fractals of Earth and Jupiter (778.57 106 km):
778.57 minus 149.6 = 628.97 [double pi-like]
Consider some celestial, geometrical minutiae:
Jupiter’s average distance from the Sun = 778.57 [semimajor axis 106 km]
Jupiter distance from Earth/matriX
Minimum 588.5 106 km
Maximum 968.1 106 km
588.5 + 968.1 = 1556.8 / 2 = 778.3
Earth : Jupiter = 778.3 = Jupiter : Sun
Something similar occurs with regard to the planet Mars:
Earth : Mars = 227.9 = Mars : Sun
| 227.9 x 3 = |
683.7
|
|
|
1367.4
|
[solar radiation constant 1367.6c] |
1367600 - 1366560 = 1040c [Twenty calendar rounds @ 52c years]
One cannot help but notice the ancient 676c Four Suns Legend number.
One might even consider a relationship regarding the height of the Great Pyramid:
481.5 feet x 12 inches = 5778 inches x 2.54 (cm. Conversion factor) equals 14676.12 minus 13676.00 = 1000.12
Coincidences of number abound throughout the ancient reckoning numbers:
| 481.5 x 2 |
=
|
963 | [remember the 693c figure] | ||
| 1926 | |||||
| ... | |||||
| 1972224 | minus 1959552 (Nineveh) | 12672 | |||
| 6336 | |||||
| 3168c | difference |
22. The Natural Number Series and the Maya Long Count
| 1 | |
| 3 | |
| 9 | |
| 27 | times 3 = 81 |
| 81 | |
| 162 | |
| 324 | |
| 648 | |
| 1296 | |
| 2592c | [The Great Cycle of Precession] |
| 5184 | |
| 10368 | |
| 20736 | |
| 41472 | |
| 82944 | |
| 165888 | |
| 331776 | |
| 663552 | minus 1959552 (Nineveh) = 1296000 (!) |
| 1327104 | |
| ... | |
| 165888 / 72 | = 2304 [7200 katun; 23040000000 alautun] |
The relationship of the maya long count to itself yields the natural number series.
23. The Maya Venus Counts 584c and 585c
The maya Venus counts, 584c and 585c days, are related to the maya companion number, 1366560c.
| 584 x 585 | = | 341640 |
| 683280 | ||
| 1366560 |
24. The Maya Long Count and the Kemi 756c
576 / 756 = .761904761904 [translation symmetrical number]
What if they rounded the factor off to .762
| 756 x 762 | = | 576072 | [double Maya Long Count fractals] |
| 1152144 | |||
| 2304288 | |||
| 4608576 |
One computational variation on this theme:
| 762 x 364c (day-count) | = | 277368 | ||
| 138684 - 136656 | = | 2028c [Four Suns] |
25. The Precession (25920c) and the Nineveh Count (22680c)
25920 / 1.142857143 (diametian) = 22680.00002
26. Maya Companion (1385540) and Proton Mass
| 1385540 / 1.67262158 (proton mass) | = | 828364.2974 | |
| 1656728.595 | |||
| 3313457.19 | |||
| 6626914.38 | [Planck’s Constant 6.6260755 fractal] |
27. The Sothic Cycle (1.649457812) as a Power
The ancient Maya system is a base-twenty system. Now, let us utilize the Sothic Cycle number as an expression of that system to the power of 1.649457812
| 201.649457812 |
=
|
139.9568277 | |
| 69.97841384 | |||
| 34.98920692 | |||
| ... | |||
| .13667659 | [calls to mind 1366560 Maya] |
Let us employ the fractal for the neutron mass as a power for the twenty base system:
| 201.67492716 | = | 151.0533898 |
| 75.52669489 [Great Pyramid baseline 756c] |
In the base ten system, the Sothic 1.649457812 power yields significant numbers:
101.67492716 = 1.461994643 [The Sothic Cycle 1460c – 1461c]
28. LOG Sothic 549.81927
| LOG 549.81927 | = | 2.740219957 | |
| 1.370109978 | [inverse fine structure constant 1.370359895 fractal] |
29. LOG Nineveh 1959552c
| LOG 1.95952 | = | .2921567927 | ||
| .5843135854 | ||||
| 1.168627171 | ||||
| 1168.6271712 | = | 1365689.465 minus 1366560 = 870.5352 |
30. LOG 91.104
LOG 91.104 = 1.959537445 [1959552c Nineveh]
31. LOG 236
| LOG 236 | = | 2.372912003 | |
| 4.745824006 | |||
| 9.491648012 | |||
| 18.98329602 | [calndar round 18980c days] |
The 236c is to be found in the Dresden Codex with regard to the day-count of Venus.
32. Square Root of the Reciprocal of Seven
1 / 7 = .142857142857142…
 142857 |
= | 377.964284 | |
| 755.9285681 | [756c baseline Great Pyramid] |
| The Great Pyramid: | East side measurement | 755.88 feet |
| West | 755.77 | |
| North | 755.43 | |
| South | 756.08 |
| 755.9285681 / 2 | = | 377.964284 | |
| 188.982142 | |||
| 94.49107101 | |||
| ... | |||
| .001441819 | [baktun : 1 : kawil] |
33. The Precession Count as the Maya Long Count Period
The precession period based upon 26000 years times 365.256 days would yield a count of 9,496,656 days. If we subtract from this number of days one-tenth of the maya companion number, 136656, then the following obtains:
9496656 minus 136656 = 9360000 days
The Maya Long Count period has been cited as being 1872000 days.
9360000 / 1872000 = 5
The Maya Long Count period would represent one-fifth of the modified precession count of 9360000 days. As we remember the legend of the Five Worlds, of the Five Suns, then, the figures become highly suggestive. One could imagine five worlds of 1872000 days each to complete the precession cycle.
34. Some Relations for the Day-Counts and the Precession Cycle
| Days |
260
|
354
|
360
|
364
|
365
|
365.256
|
| Years 25920 |
6739200
|
9175680
|
9331200
|
9434880
|
9460800
|
9467435.52
|
| 25956 |
6748560
|
9188424
|
9344160
|
9447984
|
9473940
|
9480584.736
|
| 26000 |
6760000
|
9204000
|
9360000
|
9464000
|
9490000
|
9496656
|
| 25800 |
6708000
|
9133200
|
9288000
|
9391200
|
9417000
|
9423604.8
|
The significance of the 9360000 precession number becomes evident for both the 260c and the 360c ancient Meso-American calendars.
9360000 / 260c day-count = 36000 years
9360000 / 360c day-count = 26000 years
9490000 x 2 = 18980000 / 18980 = 1000 calendar rounds
9360000 / 1872000 = 5 Maya Long Count periods
1366560 / 1872000 = .73 of a Maya Long Count period
Now, consider:
9496656 - 1385540 = 9358102 - 9360000 = 1898c [calendar round]
9360000 / 819 (kawil) = 11428.57143 [diametian based on pi as a reciprocal of seven number 3.142857]
35. Maya Precession 25956c and the Great Cycle 25920c and the Proton : Neutron Mass Ratio
25956 / 25920 = 1.00138888889
Neutron : Proton Mass Ratio = 1.001378404
The ancients appear to be choosing ratios of precession numbers that follow on the heels of ratios within other levels of the existence of matter and energy.
36. Ephemeris Time and the 3168c
1 / 31556925.9747 = 3.16887646415
One may wonder whether the Maya were off regarding their 25956c precession figure, until we double the Ephemeris time number:
| 3.16887646415 | |
| 6.3377529283 | |
| ... | |
| 202.808093704 | [On the way, we observe the 2028c Four Suns number] |
| ... | |
| 12979.717997 | |
| 25959.435994 |
37. The Megaparsec: 3.26 Million Light Years
The radian may help us understand the possibility of a 260-degree circle and a 374.4-degree circle, both of which the ancients may have employed according to the numbers coming out of the ancient reckoning system.
The 360-degree circle is customary for us today.
| 360 / 57.29577951 | = | 6.283185308 |
| 3.141592654 [pi as expressed today] |
The 260-degree circle:
| 260 / 57.29577951 | = | 4.537856055 |
| 2.268928028 [Nineveh 2268c; ancient pi] |
The 374.4 degree circle:
| 374.4 / 57.29577951 | = | 6.53451272 |
| 3.26725636 [relational pi] |
The 3744c figure comes from doubling the Maya Long Count period fractal of 1872c; and, one immediately notes the relationship to the fractal expression of today’s Megaparsec, i.e., 3.26 million light years.
38. The Maya Long Count Period and a Possible Relation to the Sothic Cycle
The Maya Long Count period is deemed to have been 1872000 days. Let us take half that figure and carry it to the seventh power:
| 9367 | = | 6.294060906 | [fractal floating decimal] | |
| 1.258812181 | ||||
| … doubles to | ||||
| 1.64995030214 | /3 = | 5.49983434046 fractal | ||
The 549.983434 figure reminds us of the Sothic 549.819270666 figure.
549 - 819 = 270549 - 983 = 434
549.983434046 - 549.819270666 = .16416338
| 549.983434 - 549819270 |
=
|
164164 | |
| 328328 | |||
| 656656 - 136656 = | 520000 |
39. The 354c Day-Count Calendar and the Sothic 693c Count
| 354 x 693 |
=
|
245322 | ||
| 490644 | ||||
| 981288 | ||||
| 1962576 - 1959552 (Nineveh) |
=
|
3024, 1512, 756c |
40. The Maya Companion Number Flows Naturally from the 576c and 756c
| 756 x 576 | = | 435456 |
| 1306368 | ||
| 3919104 | ||
| ... | ||
| 1.36650706916 |
If exactly 1366560 fractal, then, after reverse engineering, we reach fractal, where 576c remains invariant and 756c varies:
435472.87 / 576 = 756.0292882 [south side Great Pyramid 756.08 ft]
41. The Great Pyramid: Height Times Base Equals Earth Day-Count
We may take the different measurements offered for the height of the Great Pyramid in relation to its base, and devise numbers related to the concept of pi; many authors have forwarded such analyses. However, one may also contend that the relationship of the height and base length of the Great Pyramid could be communicating the day-count of Earth. Only a few examples are required to comprehend the manner in which adjustments could be made in order to achieve more exact rlationships.
378 feet (half the base length)
481.5 feet (height of the Great Pyramid)
378 x 481.5 = 182007 [fractal]756 x 481.5 = 364014 [day-count of 364c days fraction/fractal]
Variations and adjustments could be then made:
365250 / 756 = 483.134921 [fractal]
365250 / 481.5 = 758.5669782
Any number of adjustments in the relationship may be effected by changes on one side of the equation or the other. The significant point in our minds is to observe how the measurements of the Great Pyramid continue to offer distinct ways of viewing relationships within Nature.
42. Observations
This essay has presented only a few of the relationships that we have been exploring within the ancient reckoning numbers. There are many more to come. However, we thought that it may be suitable to offer a few of the more outstanding relationships before presenting more extensive themes on related subjects.
© 16 July 2001-2003 Copyrighted by Charles William Johnson. All rights reserved. Reproduction prohibited without the express written permission from the author.
Earth/matriX: Science in Ancient Artwork, P.O. Box 231126, New Orleans,
Louisiana, USA,
johnson@earthmatrix.com
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