Magic Squares Cubes Diamonds and Hypercubes

This webpage is devoted to the description of two new fundamental books on the topic of magic number tables.

The book essentially deals with number tables that are square, cubic, and hyper-dimensional. The numbers, taken from a sequence from 1 to N, used only once, are arranged in a square or rectangular array so that every row, column, main diagonal in both crisscross directions and all wrap diagonals, sum to the same number. These number tables contain geometric, dimensional equality summations that are extended to the 5^th dimension. Establishing that these profound mathematical discoveries are more spatial than numeric in nature, the book addresses just what implications they may have for manifesting the structures of real space and proffers some challenging and original notions when it comes to relating these mathematical discoveries to the basic design and functioning of the universe. It claims time is a specific frequency of the dimensional level and not in itself a dimension. It subsequently discusses the implications this has for faster than light-speed travel and for penetrating the 4th dimension.

The book proves by both demonstration and logical argument that there exist no methods in mathematics that can impose upon the elementary series of natural numbers the profound and pervasive equal-summation patterns depicted herein; that the magic number tables are pre-existing intelligent design patterns.

The second book is a derivative of material in the first:
The Atom is a Product of Superior Intelligent Design
Here's Positive Proof

This book develops for the first time ever a plausible basis for the pattern underlying the number of elements in each row of the Periodic Table of Elements, namely the series {2,8,8,18,18,32,32}. Atomic physicists have yet to offer an explanation for this particular numeric pattern.

This feat is accomplished by showing that magic squares and magic cubes hold the answer. These fundamental, tightly connected patterns that exist among the series of consecutive natural numbers are shown to be of superior intelligent design, i.e. to be beyond human intelligence to fabricate.

It then follows that the basic fabric of space, being of an exceptionally complex weave, must itself be the scaffolding upon which the atoms are built. Consequently the structure of the atoms is a result of superior intelligent design.

The number and location of octals incident to the characteristic spheres in a series of perfect magic cubes are demonstrated to correlate 100% with the number and orbital paths of electrons in the outer electron-shells of the noble elements.

Continuous complementary characteristic tiling patterns hidden within prime-number-size magic squares are exposed for the very first time. These are found to provide the missing links needed to explain and account for the number-pairing of electron-counts between pairs of adjacent electron shells in atoms.

This is the first time that such a profound connection between magic number tables and the real physical world has ever been made. And it's proven mathematically to be a product of superior intelligent design!

Both 26-page books contain identical content. Click on either buy-button to access an 8-page preview.

Magic squares are square tables composed of the number series 1 thru n², each used once and only once, and arranged so that all the rows, all the columns and all the diagonals separately sum to the same number, called the square's characteristic number. While at the same time, all the rectangles symmetric about the center have equal sums that are a specific fraction 4/n of the characteristic number.

Currently, magic squares are considered just recreational trivia, mere anomalies which clever people concoct from the series of consecutive numbers just mentioned. They are predominantly confined to just two dimensions and have rarely been devised for cubes.

This book takes these magic number squares to a whole new level by three orders of magnitude. The magic aspect of the number squares is viewed not as the property of the numbers but as the property of the space in which the numbers reside. The properties that are seen in 2-dimensions are shown to exist in all higher spatial dimensions and for every size table, on and on toward infinity. Limited by print legibility, they are demonstrated only up through 5-dimensions.

Moreover, these same summation properties and geometrical relationships that are seen to apply to magic squares are also demonstrated to hold for magic diamonds. These have never been seen before this. Their very existence confirms that the demonstrated properties are more of a spatial nature than a numerical one!

The pervasive but distinct equality-patterns prove mathematically that multi-dimensional space itself exhibits portentous signs of an underlying intelligence. Specifically, the multiple cross-directional summations within a consecutive number series, arranged in a square, rectangular table or diamond, the former two geometries spanning multiple dimensions, all adding up to the same characteristic number for its size and type, is clearly not just happenstance. It is a pre-existing design property of space.

The number of geometrical patterns which sum to the same value throughout the entire table expands with each added dimension. Herein lies the first exposure to a hidden universal manifold, a bloom that blossoms more and more as the number of dimensions increase.

If you have a keen interest in magic number tables, you will find this book not only interesting, but essential reading --ignoring this book will only be at your own expense. The majority (96%) of what is demonstrated and the presentation of it in pictorial format is new material not seen before. Read the table of contents and see if you have seen this addressed anywhere else.

Here to the right is the perfect size-5 magic square. It is composed of numbers from 1 thru 25 = 5²^.

· It has all its rows, columns and diagonals summing to 65, its characteristic number.

· Its central number equals 13 = 65/5 = 325/25 and is the dimensional average of the sum of all the numbers in the square.

· Every symmetric pair of numbers, each number opposite and equidistant from the center, equals 26 = 2 x 13. This

is a property that holds for all odd-size magic squares but not for all even-size magic squares.

· Every set of 4 numbers, called quadrals, corresponding to a rectangle symmetrically located about the center, including diamonds, sums to 52 = 4/5 x 65. Although that is an obvious corollary to the previously stated property, the previous property does not hold for half the magic squares of even-size, whereas this latter one here applies to magic squares of all sizes and is therefore a general property for 2-dimensional squares.

Moreover, this 5x5 square is magic-perfect by reason of the fact that all the row, column and diagonal summations are equal to 65, and the sums of all rectangular-spaced numbers about the center, including diamonds, are equal to 52, a specific fraction, 4/5ths, of the characteristic number 65 for the size-5 square.

Now, observe that every "+" and "x" in the size-5 magic square also sums to the characteristic number 65. This is called a complementary pattern in that two distinct patterns occur simultaneously. Not only that but these patterns interlock into a tiling pattern for the entire table. They can be dragged across the table and wrapped onto the opposite edges and still the patterns sum equally to the characteristic number. Every number in the table can function as the center of either tiling pattern.

There are more of these characteristic patterns than there are row, column and diagonal equality summations combined by an order of magnitude. Whereas there are only 20 linear summations here, there are 50 pattern summations equaling the size-5 square's characteristic number. The book depicts these unique hidden tile patterns for every prime-number-size magic square from size 5 thru 31. These hidden characteristic patterns have never been detected nor seen before this.

For the first time ever, a perfect size-9 magic square is shown. It was obtained from collapsing a size-3 hypercube in 5-dimensions, the only way it could possibly have been discovered. It is shown in full on the front cover of the book. If you want to see it in full, you need to go to the POD publisher website Lulu.com by clicking the buy-this-book link below and observe the bare cover.

At right is a size-6 near-perfect magic square. It is the first time the size-6 magic square has been depicted with all its diagonals equal to its characteristic number.

Near-perfect squares are only a hair’s breadth away from being perfect – these squares have only two rows which do not sum to the characteristic number but differ from it by ± n/2 amounts.

Equality in these two unequal rows can be obtained by merely swapping one pair of numbers from a single column between the two unequal rows whose difference corrects the amount of row-inequality (purple-shaded cells). Making any of these exchanges, however, then trades two row-equalities for four diagonal-inequalities in complimentary minor and major wrap-diagonal sums. It’s a choice of having all row-equalities or all diagonal-equalities, but not both. There are more equalities in the near-perfect form so that’s the nearest to perfect status that they come. Outside of this, it possesses all the other equality relationships ascribed to perfect status.

The chapter on standard magic squares gives complete tables for magic squares from size 3 thru 31 and shows that all but size 3 and 4 are perfect or near-perfect. It also shows the periodic pattern of the near-perfect squares among all perfect magic squares up to size 114. The series demonstrates that the pattern is repetitively infinite.

A brand new kind of magic square, called the matchmaker’s magic square (mm for short), is introduced for the very first time.

At right is an example of one of size-5. Here, the numbers range from 1 thru 9 with some numbers involved multiple times.

· Every set of 5 numbers corresponding to a matching of one row to one column, with no row or column being duplicated nor omitted, sums to 25.

Every sub-square in the bigger square has identical properties, most impressive in larger size squares like the 9x9 where all 362,880 possible matchings are equal and all 40,320 possible abbreviated squares of size 5 (smaller squares derived from the larger square, for example, from selecting any 5 rows and any 5 columns independently of each other) have the same properties. This holds for any size abbreviated square.

The chapter on matchmaker's magic squares shows these kinds of magic squares for sizes 4, 5 and 9; a size-4 magic cube; and a size-5 magic hypercube of 4-dimensions. Because it is such a simple procedure, the chapter on mm-squares also shows how to construct this kind of square for any size and across as many dimensions as you like. It also describes what constitutes a matching in cubes and hypercubes.

When this kind of magic square is put in normalized form, it is shown to have many of the general properties of the regular magic square of the first kind eventhough it has a different range of numbers and a unique set of properties all its own!

Shown for the very first time are magic diamonds. They are always of odd size. They involve the numbers 1 thru N used once and only once. The pivot number is always central and is the average of all the numbers in the table. Their rows and columns or diagonal sums are multiples of the pivot number according to their respective lengths. The symmetric pairs always sum to 2 times the pivot number. Their characteristic number is always their size-multiple of the pivot number.

There are two distinct types of magic diamond: one where the rows and columns all sum to a multiple of the pivot number, called the grid-sum diamond or just magic grid diamond; and the other where it's the diagonals which sum to a multiple of the pivot number, called the crisscross-sum diamond or just magic crisscross diamond.

The pivot number is 43, the 2-dimensional average. The diamond's characteristic number is 559 ( = 13 x 43). Each row and column excluding the extreme ends sums to a multiple of 43. Both major and minor diagonals of the largest embedded square sum to a multiple of 43. That multiple is the number of cells in the row, column or diagonal.

The colored sections sum to the numbers at left. Each sum is an exact multiple of 43 and these multiples sum to 85 the largest number in the table, N.

The pivot number is 57, the 2-dimensional average. The crisscross diamond's characteristic number is 855 ( = 15 x 57). Both the central row and central column sum to the characteristic number 885 . All the major and minor diagonals sum to either 456 or 399, a multiple of 57. That multiple is the number of cells in the corresponding diagonal.

Every symmetric pair sums to 114. So every quadral sums to 228 ( = 2 x 114 = 4/15 x 885). The sum of all the quadrals (7+6+5+4+3+2+1) x 228 = 6384 is an exact multiple of the largest number in the table less 1, namely 112 So adding in the pivot number for completeness, all the numbers in the diamond sum to 6441, an exact multiple of 57, namely 113 , the largest number in the table, N.

While these equality sums have been obtained for magic diamonds, all of this is the same as for the odd-size magic square of the same size! Their generalized formulations are identical! These are general equal-summation properties that hold in common for every pair of both types of magic diamond and both types of magic square of the same size.

Cubic number tables are easily viewed as a sequence of block-squares stacked like cards in a deck of cards. Each block-square is a left-to-right vertical planar slice through the cube. View the top square as the furtherest from the front of the cube and the bottom square as the front of the cube facing you.

Below at right is the absolutely perfect size-5 cube of numbers 1 thru 125 = 5³. Observe that for the 5x3D cube:

· All the planar levels from top to bottom add up to the same number 1575 (sum of identically located rows among all block-squares).

· All the six planar main diagonals each add up to 1575 (the sum of identically located diagonals among all block-squares).

· All of the planar-wrap diagonals in all six directions (two crossing each of the three axes) sum to 1575 –

making the cube absolutely perfect.
(All not shown here.)

· Every octal (pair of identically located quadrals from oppositely positioned block-squares) adds up to 504.

· Each of the only two possible octahedrons

sum to 378 = 3/4 x 504. (crimson and plum colored cells)

· The central pivot number is 63, the dimensional average of all the numbers in the cube.

All these relationships are correlated with a list of formulas for the size table at the end of each table’s section.

The chapter on cubes shows perfect magic cubes for sizes 2 thru 11. All magic cubes shown, except the size-10, are absolutely perfect! It is outlined there just how the size-10 magic cube can be manifested absolutely perfect by going into the 4th dimension and collapsing that magic table along its B-axis by taking depth-sums.

The picture at right shows what a 4-dimensional table looks like after it is contorted into a torus. The spirals depict the major diagonals in the table. (See: http://markorodin.com for the current 4-dimensional mathematical configuration of the universe.)

The picture below right depicts what a 4-dimensional box looks like in 3-dimensions so you can relate the individual embedded cubes in the hypercube with interlaced cubical blocks of numbers in the hypercube's table, below left.

Recall from the preceding section that cubic tables are rectangular, so these embedded cubes overlap in the 4-dimensional table just as they do in the 4-dimensional view of cubes at right. The reason there are 10 cubes in the table and only 4 in the picture below is that there are multiple embedded cubic tables passing through each 4-dimensional cubic representation, just like multiple smaller boxes contained in a bigger shipping box. The center of the table corresponds to the center of the torus and is the common point among all 4 dimensions.

The book has two chapters on hypercubes. Perfect hypercubes are shown from size 2 thru 7 in 4-dimensions and from size 2 thru 5 in 5-dimensions in very easily observed number arrays of 2-dimensions.

One of the fundamental discoveries revealed in the book is that of the continuous modularity property of 4-dimensional tables: Given a 4-dimensional magic table of size n (n² by n² table) it is shown that every contiguous block-square of size n by n embedded anywhere in the table sums to the same characteristic number of the table that all the rows, columns and diagonals do. There are some real surprises discovered there that are not revealed here in this synopsis!

Even though the subject is somewhat technical, it is presented in a systematic manner so that most intelligent readers can readily understand it without becoming stymied by the lack of a math background. Although it is number-based, it is the patterns of summation equalities that are important, not the numbers per se. A liberal use of consistent coloring (or in the case of black & white, different shades of gray) is employed to identify equality patterns throughout the presentation thereby freeing the reader from performing the many additions that would otherwise be involved to observe the equal summations. Only a few spot-checks along the way will suffice to understand and confirm what’s being presented.

Nonetheless, everything is spelled out; so for the perennial insipid doubters, it’s all there for a thorough re-examination. And the number of equality summation patterns is maximized including characteristic circles in squares, characteristic spheres in cubes and characteristic toruses in 4-dimensions (doughnuts). For the given number of dimensions, there can be no more basic summation equalities than those demonstrated for each and every magic number table.

These tables were printed directly from Microsoft Excel program immediately after the summations were verified so any error is highly improbable. I'll stake my reputation on it because I'm the one who did the calculations and verification of every table in each book and personally transferred the tables either directly to Microsoft Word or indirectly through Adobe Photoshop when they were too large for Word to handle. I made no shortcuts nor assumptions; everything was verified.

Every size table that can be printed on one or two 8½x11 pages is depicted in readable detail. In fact, the only exception is the size-5 square in 5-dimensions; if it was to be printed at all, had to be printed in a fashion that its 5 embedded quadracubes were spread over five consecutive pages and that is as far as it is possible to go and still maintain legibility and coherence.

I have relegated the general algebraic formulas to the end of each table's section in a summary list where you can see the algebraic pattern among all the different equalities that were enumerated, in just one table. The more formal formulas were relegated to the Appendix.

Reading the Appendix is not necessary to grasp the big picture, but for those who have had at least an introduction to high school algebra, the Appendix is very enlightening. It deals formally with proof by induction -- the only acceptable way to prove that an observed progressive numerical pattern is indeed universal. In fact, to make the proof on such a broad level, both table size and dimension, the description of the proof-by-induction had to be revised to include both complex patterns and two-fold sequences.

In the Appendix, it is proven that these number arrangements are pervasive throughout any number of dimensions and are the properties of space and not just the properties of the numbers. The Appendix serves well as a teaching guide for demonstrating how patterns are formulated and then unified into generalized formulations.

This book demonstrates that there exists an underlying pre-existing numerical pattern of space that is not only consistent and pervasive but, since the measures form a progressive pattern themselves, are of definite intelligent design.

The book contains a lot of new information and many neat ideas never discussed anywhere before. Don't let anyone claim otherwise. Click here to view the Table of Contents.

To make the case for an intelligent pattern underlying multidimensional space, there is no need to address the details of all the methods that were used to uncover these number patterns; only the existence of intelligent patterns need be demonstrated – and that’s what the book is all about. It is 261 pages of solid discovery, including the informative Preface, Foreword and Glossary.

Let me remark: I didn’t invent these numerical tables – I discovered them just as the first prospectors discovered oil. These discoveries of pre-existing conceptual patterns underlying square and rectangular number arrays of the natural number series is way more than my mere creative handiwork; it is something much more fundamental on a cosmological scale. It says something profound about regular and hyper-dimensional space.

These equality properties hold for all sizes of number-tables from 1 to infinity and have existed ever since the beginning of time, if in fact there was such a beginning. They were only discovered recently between January 2005 thru August 2009 through the use of my PC computer employing Microsoft’s Excel program; they were not invented nor constructed from imposed patterns like all the limited published work on magic squares so far. The computer functioned as my microscope, my eyeglasses, my telescope and, as you will see in the Postscript, also my transporter. This book lets you see what I saw in the grandest fashion with very little effort.

It is demonstrated by showing numerous specific examples in a continuous series that multi-dimensional space can be measured and mapped by three distinctly different measures and yet still independently exhibit identical dimensional geometric equality patterns among all the dimensions. Specifically, the multiple cross-directional summations within a consecutive number series, arranged in a square, rectangular or diamond table spanning multiple dimensions, all adding up to the same number is clearly not just happenstance, nor is it a predictable or contrived occurrence. And all the embedded block-squares in higher dimension tables summing to the same number in addition to the summations just cited is not something that can be concocted. There are consistent equality patterns so complex that it is beyond human intelligence to fabricate them. They are an intellectual design property of space as well as major fundamental discoveries.

The number patterns manifested herein stand on their own without having to resort to unrelated non-numerical patterns such chess-board moves of the knight or sacred science for their manifestation. Moreover, the patterns that emerge are not strictly numerical either; they are shown to be essentially the property of space itself. Furthermore, these astounding equal-summation properties also have implications for the very structure of the universe.

For example, when our universe is viewed from outside itself, the current scientific model of a 4-dimensional universe can be described by a torus. The book shows that 4-dimensions can be measured and mapped by perfect magic 4-dimensional quadracubes.

Besides making the case for intelligent design in magic number tables, the book makes the case for intelligent design in two other instances, one in astronomy and one in atomic physics: in the spacing of planetary orbits in our solar system and in the number of elements in each period of the Periodic Table of Elements, neither of which has been recognized heretofore.

Proof positive is given in Part VIII for the 100% correlation between the number of octals summing to the characteristic number in the series of characteristic spheres corresponding to magic cubes of size 4x and the number of electrons in the outer shell of the noble elements in the Periodic Table of Elements!

The book demonstrates a fundamental principle never before recognized: that the "beyond-perfect" magic squares of prime-number-size possess unique tiling patterns where, in addition to all the rows, columns and diagonals in both directions, all the individual tiles each sum to the square's characteristic number. These tiling patterns occur in pairs simultaneously. They are shown to account for the pairing of electron counts in adjacent electron shells of the noble elements! Scientists have yet to offer a rational explanation for this phenomenon. This is proof positive of intelligent design patterns underlying real sub-dimensional space.

These natural-number summation-equalities that arise again and again in larger and larger tables and in higher and higher dimensions from increasingly multidimensional perspectives can only be attributed to the pre-existing intelligent design of multidimensional space.

This book is not intended to be a proof of creationism trumping evolution. It is merely a numerical exhibition that there is definitely an intelligent numerical order underlying multi-dimensional space, viz, virtual space. Amazingly, these intelligent patterns actually have correlations with the physical universe.

Recognition of intelligent patterns also applies to other patterns observable in our world too, like the order in the structured pattern of elements from neutrons, protons and electrons; in the structure of subatomic particles like the neutron and proton all assembled from different combinations of three out of four different elemental quarks; and in the spacing of planetary orbits around stars. All these too are universes unto themselves, discovered only in the last century, each with the portent to be a product of intelligent design.

Table of Dimensional Levels
Dimensions	Description (examples)
4	Hyperspace (multiple universes)
3	Cubic space (galaxy, star, planet, moon, skyscraper)
2	Planar space (planetary surface, ocean, lake, billiard table)
1	Linear space (lazar beam, optical fiber, wire, string, measuring tape)
1/2	Molecular level (DNA, enzyme, nucleotide, prion)
1/3	Atomic level (hydrogen, mercury, uranium)
1/4	Sub-atomic level (electrons, protons, neutrons, particles)
1/5	Sub-particle level (quarks, leptons, hadrons)

The book demonstrates that the 4th dimension is very likely real since it can be measured and mapped by 2 distinctly different magic number tables. If so, our universe contains at least four co-existing 3-dimensional universes simultaneously. With that understanding, the book disputes the concepts of an ever expanding universe, dark matter and the Big Bang theory by showing that there are alternate notions within a 4th dimensional framework that involve simpler physics. Despite all the mathematical scaffolding constructed by physicists to support these current-day notions, they are limited by the assumption of a 3-dimensional universe. Under this myopic assumption, such mathematics has been concocted to support a belief system that is based on improvable and unfathomable principles.

Students especially need to be able to recognize the patterns in scientific knowledge as it is presented to them and question their teachers about just where do they think such order came from. The typical answer might be that such order is the product of Man's conceptual classification and may not be real, but this notion is totally inadequate. If such order exists, it was there before Man recognized and organized it for himself! So just how did it originate? This subject begs to be addressed during the educational process and not sloughed off.

Not only that, but by looking for the often times hidden patterns of intelligence, we are able to discover even more fundamental relationships than are initially manifested. My book is one prime example of that -- if I were not inspired by my initial discovery of an amazingly simple process for manifesting perfect magic squares for all the prime number sizes greater than 3, I wouldn't have bothered to find manifestation processes for perfect magic squares of the remaining

composite sizes, nor yet taken the search beyond 2-dimensions.

The crop circle at right has an inherent intelligent design pattern: it pictorializes the number pi out to 8 decimals. Given the schematic overlay, that should be obvious. However, there's more intelligence in this schematic hidden in the distribution and sizes of the circles than is first evident. Note that the largest circle at the center is 5 units. The circles at the top are 4, 3 and 2 units in diameter. The circle at the end of the "start" arc is 1 unit.

What this pattern implies is that the number sequence continues beyond the decimal point indefinitely even though it is rounded off when it gets to the "end".

Science tries to answer the "What". Mathematics tries to answer the "How", the "Why" and the "means". The broader we look, the more we find initially structured, pre-existing fundamental intelligent order on a grand scale. Now, it has been found extensively in the spatial patterns of numbers.

A crop circle appearing out of the pitch of night in Wiltshire UK on June 6th 2008.

If there is to ever be any basis for a Mastermind’s shaping of the universe, this book furnishes that basis by demonstrating the pre-existence of pervasive numerical and geometrical patterns which are purely an intellectual product that no one can deny. And it's all there for you to see for yourself.

The academic community has been mute upon encountering my book. They are stunned by this revelation, still searching for a counter-example or a means for producing these magic number tables by imposed formulas. They will never succeed. I've proven mathematically that it can't be done. So whence did these amazing pervasive equal-summations originate? Surely not from the mind of Man.

This book breaks new ground that is light-years beyond what ever has been published anywhere else before. Here's my guarantee: if you don't find that the material presented in my book is not what I claim it to be, you show me proof of purchase and return the book to me for a full refund. OK?

I hold Mathematics Degrees from Penn State University (BS 1964) and Stanford University (MS 1971) with a good foundation in the sciences.

My Masters Thesis at Stanford unified a whole field of divergent mathematics and covered over 160 pages of formulas and tables. Prior to that, many practitioners in the field were putting their own spin on the topic. That practice ended after it was given a common methodology with the publication of my Masters thesis as a book by US Steel Corp. entitled Decomposition of Large Scale Systems for All Known Structures (Library of Congress ref no. A417086, reg. 3/15/73). I've done the same thing here in this book with magic number tables.

In the course of my inquiries into mathematics, any topic about which I have written has involved large expositions. The basis for this, I presume, is just my being in the right place at the right time. On a number of occasions over the years I have haplessly stumbled into vast unexplored territory, whence I have been privileged to get to the legendary conceptual mountain top where the whole subject, as far as the mind’s eye could see, was revealed to me. And my writing about it had to cover so much virgin territory just to establish the basic principles by which the topic could be adequately explained that there was no way I could confine my description to a few concise pages in a mathematics journal. (All remain unpublished because the professional math journals would allot me at most 6 pages in their precious paperbacks! The definitions alone would consume that amount of space.)

Explaining the topic of measuring and mapping space here is no different. Any previously published work on “magic squares“ is so myopic and the field of numerical spatial analysis so virgin that its presentation had to be broadened to establishing first-principles first. It takes many consecutive examples to see the broader pattern for the big picture to emerge. Specifically, one has to look beyond the smaller squares and cubes to surmount the anomalies that occur there for embryonic size tables in 2- and 3-dimensions to see the bigger patterns and to get beyond those dimensions into hyper-dimensional space to see the really profound amazing relational patterns. So the smallest first-round introduction to this new subject is not just a series of published papers in a math journal, but an entire book. This book took retirement and 5 years full time to write it and get it all right.

But instead of trying to appeal to academicians, I put all the math in the Appendix for the math-men to digest and kept the presentation pictorial and in summary form for the above-average intelligent reader. I also refrained from using formal terminology that was not really informative and high-sounding although I had to invent some terminology for new concepts that have not really been addressed before.

One cannot write anything confrontational or on a topic deemed taboo to the academic establishment if it is to be ever published in any peer-review journal or by any academic press. So I write and publish my own books. At the age of 69, I am so thankful that I have never been forced to join an academic institution out of a fear of losing my source of income. I have been and still am a free agent.

One would think that the God-worshiping element of the populace would have a keen interest in this topic and the proven pre-existence of intelligent design patterns which are so way beyond human fabrication that they qualify for the designation of "divine". But to my dismay, religionists are totally ignorant of anything mathematical. They sure as hell can quote from their scriptures, but when confronted with anything mathematical they go stultifidedly mute, that is, until they manage to change the subject to their pontification of the scriptures and proselytizing.

That tells me a lot about the IQ of the religious, practitioners and preachers alike. They never studied or forgot or failed at math in school and now are incapable of appreciating something as profound as pre-existing intelligent design patterns that would confirm the existence of their creator. Whether such a creator gives a damn about their petty day-to-day problems or listens to their self-indulgent pleadings is the domain of the clerics, not a mathematician. What I have done is merely prove both mathematically and by demonstration of a ubiquitous series of specific examples that our universe was constructed with extraordinary intelligence.

Regardless of your position on the existence of a cosmic designer, if you think you know all about that subject, you're in for a real disillusionment. You can no longer deny the existence of these patterns of superior intelligent design because my book shows that they are pervasive on every dimensional level using 4 distinctly different measures. And despite the uniqueness of the patterns among these 4 different measures, they all have the same mathematical formula for their characteristic number and inherent dimensional geometries. The content of my book will profoundly change your world view just as it has changed mine, this I promise.

At right you see a perfect size-9 magic triangle. All the same-length diagonal and horizontal summations are equal throughout the table. The triangular 3-celled corners also sum equally. There is an Addendum on magic triangles that is not in the book because I only discovered how to manifest these magic triangles just recently. Further, there are no predictable inherent intelligent design patterns as there are for the rectangular magic number tables.

How can you get this Addendum too? After you purchase my book, you will receive a confirmation email from Lulu Press indicating the purchase date and the Lulu PO number. You forward that Lulu purchase email receipt to me as a forwarding email to Mr.Math@Live.com.

Upon receipt of your email, I will send you the Addendum chapter "Part IX" on magic triangles free as a PDF attachment in my reply to your email.

Note: These perfect and near-perfect magic triangles have never been seen before. They are shown in the Addendum ranging sequentially from sizes 7 thru 10. Note that there are no magic triangles below size-7. Note also that it takes a lot of guess-work and manipulation to uncover these triangular patterns. Without a fundamental pattern to follow, they are very difficult to manifest, even more so as their size increases. I could use some help.

FYI: My treatise on magic number tables is the result of a 5 year solo research and development effort without support of any kind from any institution or employment, so don't remark to me that my book is "pricey". Mathematically oriented books these days run an average of $80 and my book is the equivalent to any of those on both a textual and pictorial level. It's 252 pages of new knowledge.

People associated with institutions are supported by grants and their salaries to induce the sharing of their discoveries freely. That's not my situation here. Academicians and magic square aficionados with websites on the topic don't seem to understand that. This book was self-published at my own expense and written under my own support.

If you don't like the price, then you don't deserve to share in my discoveries. You can just go do it on your own with the knowledge that it has already been done. That's my position on it. And by the way, Good luck; you'll need lots of that to manifest what's already in my book. Actually, you will need "divine intervention".

Each page in the book is double-side printed in black & white on 8½ by 11 inch pages. It comes in a soft-cover bound version from Lulu publishers via the internet. Both the front and back covers are in full color. It's 263 pages of predominantly new material.

The book has been professionally edited for errors and omissions, proper text alignment, technical consistency, cross referencing throughout the text and position and layout of the hundred and fifty or so number tables. The tables have been computer verified for numerical accuracy. Over 85 pages are cross-referenced so you don't get lost as many later topics are interrelated or built upon earlier ones. The subject is cumulative as you go and multiple page references are made to earlier and later sections to facilitate your comprehension of the current topic.

I have prepared a PowerPointä presentation for teaching purposes. It consists of 83 full-color slides and is available on a CD for $33.95 plus $4.85 for shipping & handling (media mail) or $10.44 shipping by US Postal priority mail. Click here for a preview of some of its contents.

For furnishing students copies of particular sections for educational purposes please contact me directly. Teaching materials are not considered research materials by the Courts and the original may not be copied for that purpose; please read the copyright notice and warning below.

I am willing to give projector-screen based lectures on the topic for a fee and will only travel to do so when I am guaranteed an audience of at least 50. Lectures take 1¾ hours including a 15-minute break. See teaching materials below. If you are interested, please email me at Mr.Math@Live.com .

© The perfect size 9x9 magic square which appears on the book's cover is made public there for the very first time. All perfect magic squares are derivatives of one another. Any size 9x9 perfect magic square appearing anywhere else is a derivative work obtained by merely interchanging some rows and columns and is therefore a copyright infringement.

The tables and pictures on this page and in the book have been formally copyrighted and may not be reproduced on other websites, in presentations or other publications without written permission by the author or his authorized legal agent. These copyrights will be strictly enforced.

Warning: Intellectual property is the easiest thing to steal because nobody witnesses the immediate theft. This material is protected by 5 separate US copyrights with 4 more pending and may not be reproduced in whole or in part. Taking intellectual property without adequate compensation to the author cannot be construed as being "borrowed". If any unregistered copies of these books, CDs or portions thereof, hardcopy or otherwise, are ever discovered, both the institution and the teacher associated with it will be sued for copyright infringement in Federal or International Court.

Because of the timely filing of these copyrights within the time limits of the book's publication, any losing defendant will be required by law to pay all of the author's legal expenses. The minimum cost to the defendant these days in the US is $60,000. Is it worth the risk to you or your institution?

Reward: Anybody who is first in reporting an infringement is entitled to an immediate reward of $100 upon verification of the infringement and identification of the infringer, plus a 10% share of the judgment award or settlement. Please contact the author if you have such information -- Your identity will be held with the strictest of confidence. You notify me of the infringement and I'll take it from there. Mr.Math@Live.com