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Earth/matriXSCIENCE IN ANCIENT ARTWORK

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Extract No.19

A Mathematical Constant: 288

By

Charles William Johnson

Within the maya long count numbers/fractals, the pictun number 2880000 appears to represent a strict relationship withmilar fractals occurring in nature and in the general field of mathematics. It is understandable that many scholars shyway from the study of numbers, because one does not know what particular aspect obeys human design and whichspect obeys merely the manner in which numbers behave. In the  Earth/matriX series, we have been attempting tostinguish these two aspects; numbers/fractals that occur in nature, and numbers/fractals that are historicallygnificant (chosen by the ancients in their reckoning systems). Regarding the number/fractal 288, which lies on theaya long count series (36, 72, 144, 288, 576, 1152, 2304), we shall examine its relationship in some aspects of nature

nd mathematics. The case may be that the ancient maya chose the long count series of numbers/fractals because theyflect not only a constant series within mathematics, but also because they may be found in nature.

nitially, then, we find the 288 number/fractal within the maya long count series. We have also seen this particularumber/fractal become instrumental in the arrangement of electrons in the elements of the periodic table (Cfr.,

arth/matriX, Nos. 61 & 62). The extranuclear electron count for argon is 2•8•8, with a change of level occurring withe next element,  potassium with the 2•8•8•1 arrangement. Let us observe a partial view of the periodic table, with

ome of the elements and their corresponding extranuclear electron count.

1 2 3 2 7 2 8 3 2 8 7 2 8 9 2 2 8 13 2 2 8 18 1 etc

2 2 4 2 8 2 8 4 2 8 8 2 8 10 2 2 8 14 2 2 8 18 2

2 1 2 5 2 8 1 2 8 5 2 8 8 1 2 8 11 2 2 8 15 2 2 8 18 3

2 2 2 6 2 8 2 2 8 6 2 8 8 2 2 8 13 1 2 8 16 2 2 8 18 4

he element neon has a configuration of 2•8, which changes with sodium 2•8•1; then, argon 2•8•8, which changes withotassium  2•8•8•1. From the perspective of the logic of numbers, one would expect the 2•8•8•1 pattern to evolverough 2•8•8•8; but, change occurs scandium 2•8•9•2, whereby the third level of electrons jumps to 9. Nonetheless,e significant pattern involves the 2•8•8 beginning, and the fact that it is maintained throughout with changes at theird level. No matter what, one obtains the impression that 2•8•8 is the underlying pattern suggested from the outset of e extranuclear electron count of the elements. In other words, the pattern that is visibly suggested, and broken, is that

f 2•8•8, for whatever reasons of the possibility/impossibility of electron stability at the third level.

nother example of the mathematical constant 288 exists within geometry and the relationships of 

quivaleny/inequivalency of the numbers of perfect right triangles. We have discussed this particular aspect in detail inrevious essays (Cfr.,  Earth/matriX, Nos. 55, 56, 57 & 58). The regular, perfect right triangle series begins with theeasurements 3•4•5. These measurements serve as the basis for the Pythagorean Theorem, whereby the square of therst two numbers, combined, equal the square of the third term. There exists another series of perfect right triangles,

hich may be determined as irregular, which begins with the measurement numbers 5•12•13, which also obeys theythagorean Theorem. Now, consider the difference between the numbers of the two distinct series of perfect rightiangles:

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As one may observe from this series of numbers and differences, the 2•8•8 initialterm begins the series with 2•8•8, with increments thereafter of 2•4•4. In 3 otherwords, two distinct series of perfect right triangles exist; one begins with themeasurements 3•4•5 and the other with those of 5•12•13; and, the differencebetween these measurements is 2•8•8. As in the periodic table, we are observingnow in geometry the reoccurrence of the terms 288 as an initial constantrepresenting a change in level; a change from one series of of perfect right trianglesto the other. In previous studies we have seen how the 3•4•5 and 5•12•13 numberson a graph at right angles reflect the very design and layout of some of thepyramidal sites (Cfr., Earth/matriX, No.80).

Aside from these aspects of nature and mathematics, there might be a more directbservation of the significance of the 288 number/fractal within the maya long count system itself. In order to discernis point, we shall require examining the method of duplatio/mediatio  and the maya companion number 1366560.rom the previous example, it is relatively easy to see that in order to go from the first series of perfect right triangles•4•5) to the next series (5•12•13), must simply add 2•8•8 correspondingly to the numbers of the first. Regarding theaya companion number, 1366560, its significance is not so readily observed. In fact, today scholars do not appear to

e in agreement as to exactly what the companion numbers mean (1366560 and 1385540). However, we have beennalyzing them in relation to the maya long count and the ancient reckoning system of ancient kemi, and someomputations appear to be relevant involving these particular numbers. Let us concentrate on the 1366560 companionumber here.

et us take two historically significant numbers, 25920 and 31104, and add them together for the sake of an example;en, we shall apply the doubling/halving method, and have the companion number enter the scene as well. Many

xamples may be chosen, but we shall offer only a couple, since once the reader observes the manner in which theumbers perform, it will be seen that this particular computation holds for any case. We have chosen more obviousstorically significant numbers for this illustration.

25920 57024 (doubled) 1824768 - 1366560 = 458208 458208 (halved)31104 114048 22910457024 228096 114552

456192 57276912384 286381824768 14319

14319 / 3 = 47731591

ow, 458208 / 1591 = 288

ad we continued to divide 1591 by 3, the result would have been: 530.333; a fraction. It is often stated that thencient maya avoided the fractions. In a sense, what we are observing is that their very system, the maya long countumbers/fractals, serve for computations with  fractions. The companion number intervenes at one point in the

omputation whereby a number is achieved that results in a fractional relationship with the maya long count. Considere following series based on doubling/halving the numbers:

458208 / 1591 = 288 (pictun)

/ 795.5 = 576 (calbatun)

/ 397.75 = 1152 (kinchiltun)

/ 198.875 = 2304 (alautun)

ow, let us treble the original number:

5704 1539648 - 1366560 = 173088 / 2 =171072 86544

513216 43272

1539648 21636

10818

5409 / 3 =

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601

173088 / 601 = 288

n other words, the maya long count numbers/fractals, on this particular series of numbers as of the subtracting of theompanion number, represent a constant number series, similar to that occupied by the more well-known constanteries 1,2,4,8,16,32,64,128,256,512; a series which is used in modernday computers alongwith  the maya long countonstant series (Cfr., Earth/matriX Extract No.12). The last number evenly divisible by three on the series relates as of 88x to the first number appearing on the series after the companion number has been subtracted (since 601 / 3 =00.333).

et us present one more example with a previously cited number:

290304 (= 259200 + 31104)5806081161216 - 1366560 = 205344

205344 (halved) 6417 / 3 = 205344 / 713 = 288

102672 213951336 713 In other words, after subtracting the companion number25668 237.666 1366560, one obtains a number series (fractional or not)12834 in relation to the maya long count numbers/fractals

epending, then, upon the chosen direction, the number series in these cases begins/ends with the constant term 288;s one either goes into fractional expressions (for example, 237.666), or leaves fractional expressions (for example,37.888). Prior to entering and leaving fractional computations, then, as of the maya companion number, one is alwaysealing with a number that relates 288  times with the product resulting from the maya companion number. In thisanner, from the perspective of mathematical computations possible within the designed maya long count and the

ompanion number, 1366560, one is faced with a mathematical constant of 288, which likewise begins or ends a series

f numbers/fractals based on the maya long count (36, 72, 144, 288, 576, 1152, 2304) in relation to fractional/wholeumbers.

rom this perspective, the manner in which the maya long count is designed as of  the companion number, we see aery similar procedure followed as to that witnessed within the change of levels within the extranuclear electron countf the elements as cited on the periodic table, and the translation between the two sets of perfect right triangles. In otherords, the very design of the maya long count system, as we have examined it through possible computations as of itswn terms (numbers/fractals), would appear to reflect the designs found in nature. One might want to concluderematurely that all of these relationships are mere happenstance; coincidence. Yet, the fact that an historicallygnificant number (1366560), which is obviously the result of humanly consious design and decision-making, i.e., byhoice, would somehow keep us from simply attributing all of this coincidence to mere happenstance. In order to

btain the constant series, it would appear that human intervention had to be designed as of the companion number;at is, the companion number 1366560 was chosen with a specific computational purpose in mind. It results from a

onscious design, and a specific kind of knowledge regarding the behaviour of numbers/fractals in the ancientckoning system.

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©1997-2012 Copyrighted by Charles William Johnson. All rights reserved.Reproduction prohibited without written consent of the author.

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Your comments and suggestions are greatly appreciated:e-mail: johnson@earthmatrix.com

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Earth/matriXScience in Ancient Artwork

Extract Nº.19

A Mathematical Constant: 288July 15, 1997

©1997-2012 Copyrighted by Charles William Johnson. All Rights Reserved

Earth/matriX, P.O. Box 231126 New Orleans, LA 70183-1126;USA

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