[b]WARNING!!!! HEADS THAT EXPLODE WILL NOT BE HELD ACCOUNTABLE FOR WHEN THE MODS HAVE TO CLEAN IT UP SO DONT EXPLODE![/b] Once we realize that pi represents a fractional expression in numbers, it were as though either nature itself were wrong, or the numbers must surely be able to be manipulated to render whole numbers. The ancients sought to work with whole numbers. However, once we realize that the ancient reckoning system may have been based upon the concept of a floating decimal place, then we should understand that all numbers, in fact, may be visualized as whole numbers. The cut-off point becomes one of arbitrary choice at times. With regard to the concept of pi, contemporary mathematicians have not decided to accept that arbitrary cut-off point, and continue to search for the unending decimal expression of pi. At one time, not too long ago, pi was simply represented to be 3.1416; and, in a practical sense, it served all purposes of constructing things out of matter and energy. Today, the unending expression of pi to hundreds of thousands of decimal places serves no practical purpose that we know of, at least, other than that of an unending contest to discover the ultimate expression of pi. One has only to admire the relation of the diameter of any circle to its circumference to note that particular expression. Throughout history, the expression of pi has taken on many variations. Petr Beckmann (Cfr., A History of (pi), Golem, 1971), offers an exemplary analysis of the concept throughout history. The Babylonians 3 1/8; the Egyptians 4(8/9)²; Siddhantas, 3.1416; Brahmagupta, 3.162277; Chinese, 3.1724; Liu Hui, 3.141024 < < 3.142704; Liu Hui, 3.14159; Tsu Chung-Chih, 3.1415926 < < 3.1415927; Archimedes, 3.14084 < < 3.142858 (31/7); Heron, 3.1738; Ptolemy, 3.14167; Fibonacci, = 864:275 = 3.141818; Viète, 3.141592635 < < 3.1415926537; and, finally in the computer language of FORTAN: 3.14159265358979324. Again, citing Beckmann (p.101): "There is no practical or scientific value in knowing more than the 17 decimal places used in the foregoing, already somewhat artificial, application". Now, if we consider the circumference to be divided into 360 degrees (or segments; angular divisions with lines cutting through the center of the circle as we know them), then using the contemporary figure for pi (3.141592654), the length of the circumference could be 360 units, while the length of the diameter would be 114.591559 (i.e., 360 /). Now, let us suppose that the circle is divided into 260 degrees (something that we are unaccustomed to considering, in fact). If we employ the same length of the diameter of the previous example (114.591559), then the relational figure for pi for a 260-degree circle would be: 2.268928028. With that something very intriguing developes. Within ancient Nineveh, there exists an historically significant cited as 2268. One could imagine that the 2268 fractal number may relate to the concept of proportion (i.e., pi) regarding a 260-division circle. The number 260 is relevant because during ancient times there existed in various cultures a calendar based on a 260c day-count. Furthermore, the Great Cycle of the sun, known as Precession, also involves a fractal of 260 (i.e., 26000 years). Now, were we to consider the Nineveh number for representing pi on a 260-degree circle, then the constant value for the diameter would then be 114.638448 (i.e., 260 / 2.268). Throughout history, an inexact representation of pi has always been cited as that of 3 1/7 (or, 3.142857); a reciprocal of seven number. However, when we consider that the length of the diameter of a 360-degree circle yields a number that approximates a reciprocal of seven number (114.591559), we can consider the possibility of employing 114.285714 in its place. The use of the reciprocal of seven number (114.284714) for the length of the 360 and 260 circle would offer the following values for pi, respectively: 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 day-count: 2275, 4550, 9100, 18200, 36400, etc. Also, note that the difference between the Nineveh 2268c and the pi-like 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 pi-like 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 day-count 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 well-known 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) [Edited on 9/6/2006]