- Geometrical Translations of the Ancient Reckoning System of Mesoamerica; Science in Ancient Artwork N�50, New Orleans, 1996.
- Fermat's Conjecture: the Last Theorem; Science in Ancient Artwork N�51, New Orleans, 1996.
- Related Numbers of the Maya Long Count; Science in Ancient Artwork N�52, New Orleans, 1996.
- The Maya Long Count and the Right Triangle; Science in Ancient Artwork N�53, New Orleans, 1996.
- A Critical Commentary on Chaos Theory and Fractal Geometry: the Analysis of a Snowflake; Science in Ancient Artwork N�54, New Orleans, 1996.
- Fermat, Pythagoras, and the Maya Long Count; Science in Ancient Artwork N�55, New Orleans, 7 May 1996, 13pp.Extract:
The author demonstrates how the numbers related to the maya long count may have derived from the numerical series within distinct progressions of the right triangle. The series of numbers relating to 2, 4, 8, 16, 32, 64..., and 9, 18, 36, 72, 144, 288, 576..., appear within the progressions of the 3-4-5 right triangle and the series of right triangles based on prime numbers. Furthermore, the numbers and their powers are reviewed regarding the postulates of the Pythagorean theorem and Fermat's last theorem. It is shown how the numbers of the right triangle may have avoided even the postulating of Fermat's last theorem, given the behavior of the manner in which numbers are related to the power of three on the 3-4-5 right triangle progression.
- The Maya Long Count: an Extension of the Pythagorean Theorem and an Emendation to Fermat's Last Theorem; Science in Ancient Artwork N�56, New Orleans, 1996.Extract:
The numbers related to the multiples of the 3-4-5 right triangle appear to reflect the number sets of the maya long count and the constant numbers of the 1,4,8,16,32,64,128,256, etc. progression. Furthermore, it would also appear that when the multiples of the 3-4-5 right triangle undergo relationships of equivalency to the power of three, there appears to exist a modification or extension of the Pythagorean Theorem. Also, these same computations would appear to suggest a different way of conceptualizing Fermat's Last Theorem. The fact that the numbers resulting from the charts devised by the author around the 3-4-5 right triangle seem to be directly related to the maya positional level numbers/fractals would suggest a possible manner of computation. The 3-4-5 right triangle may have served as the basis for devising and adopting the multiples of the maya long count numbers/fractal, as they both appear to enjoy the same kind of logic in the interplay of numbers; especially, the two number sets based on the 36c and the 64c numbers/fractals. The 36 x 64 combination produces the 2304 maya alautun number/fractal. Also, the addition of the two numbers equals 100 (36 + 64), which together form the twofold multiple of the 3-4-5 right triangle to the power of two: 6-8-10 to the power of two yields the 36-64-100 relation, which also serves as the logic of numbers of the maya long count.
- The Pythagorean Theorem and its Extension: the Progression of Numbers of the Right Triangle and the Maya Positional Level Numbers; Science in Ancient Artwork N�57, New Orleans, 14 May 1996, 7pp.Extract:
The maya long count positional level numbers/fractals appears to have been derived in part from the numbers established by the simple/geometric progression of right triangles; especially, the 3-4-5 right triangle. In order to illustrate this particular point, one must consider first the nature of the Pythagorean theorem x² + y² = z², and then, its extension regarding the simple/geometric progression of numbers relating to a 3-4-5 right triangle in terms of the equation x³ + y³ + z³ = x'³. In this manner, one may observe how the terms of one 3-4-5 right triangle lead to the terms of the next one on a simple/geometric progression of numbers. In other words, the terms of one 3-4-5 right triangle yield the first term of another 3-4-5 right triangle immediately following it on the progression series.
The maya long count positional level numbers reflect in detail the terms of the extension of the Pythagorean theorem. In a sense, then, the maya numbers/fractals are not characteristic of either the reasoning of Pythagoras or the maya as such, but reflect the nature of numbers established by the progression of the 3 + 4 + 5 = 6 right triangle series of numbers.
- The Pythagorean Theorem: x² = y + z An Alternative Expression for Some Right Triangles; Science in Ancient Artwork N�58, New Orleans, 17 May 1996, 8pp.Extract:
All right triangle obey the Pythagorean Theorem (x² + y² = z²), while some right triangle may also be expressed in a different algebraic manner, which is a series of right triangles derived from the 3 - 4 - 5 measurement:
x²= y + z
Much like the other progression of right triangles treated in previous essays of the Earth/matriX series, this progression of right triangles also relates to the maya long count numbers/fractals in a direct manner. In fact, the series begins as of a multiple of the maya positional level fractal 288.
- A Possible System of Multiples and Powers in the Maya Long Count; Science in Ancient Artwork N�59, New Orleans, 1996,
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