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Magic Number Squares (The Tapping, Measuring and Mapping of Multi-dimensional Space itself) Note: It has been reported back to me by book-seller stores that autistic males adore this subject and are devouring the books, Number Magic and Weaves of Wonder.
Magic Squares
Here to the right is the perfect size-5 square. It is composed of numbers from 1 thru 25 = 52. · It has all its rows, columns and diagonals summing to 65, its character-istic 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 · 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 squares of even-size, whereas this latter one here applies to squares of all sizes and is therefore a general property for 2-dimensional squares. Moreover, this 5x5 square is 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 square also sums to the characteristic number 65. This is called a simultaneous dual complementary pattern in that two distinct patterns occur simultaneously. Not only that but each of these patterns interlock into a tiling pattern for the entire table. It 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 tile pattern in the 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 square from size 5 thru 31. These hidden characteristic patterns have never been detected nor seen before this. Shown in the book is a whole new world of geonometry discovered after any perfect number square has been reduced to its modulus and integer tables (See the cover of Weaves of Wonder book below). All the prime-number size tables yield so many equal-summing string series running in four cross-directions that contain only the numbers from 1 thru n exactly once that the table takes on the role of a loom which provides for weaving many more perfect squares of the same size. And these all have dual tile patterns containing all the numbers from 1 thru n exactly once too regardless of where they are centered in their table! Next is shown another amazing property, called the sub-additive property. Below is a table where each quadrant is just a duplicate of the the size-5 square. This arrangement has been shown so that it is easy for you to verify the block-square sums of sizes 2x2, 3x3 and 4x4 with overlap across the 5x5 table's borders. These sums are then placed in a 5x5 table relative to each other. Next, the tables are reduced by the smallest number in them less 1. Observe that after normalization, either the original 5x5 square or its reflection is recovered by this process for every size block-square sum between 2 and 4. Now that's how perfect this square is. There are only two other comparable perfect representations of the size-5 square with this property which are not derivations of the one shown here.
There's yet more: observe that all the numbers in each of the four quadrant triangles in the size 5 square above sum to 195. Further, this is 3 times 65 exactly. See the size 7 square below. The corner triangles each sum to 700 = 4 x 175. All odd-size squares greater than 3 in my book have the property that all corner triangles of the same size as the square sum equally. And that sum is always a specific multiple of its characteristic number !! For instance, the corner triangles of the size 9 perfect square sum equally to 5 times its characteristic number. Do you see the pattern of the multiple here: (n+1)/2?
And there's even still more. If a table of differences between the numbers in each cell and it's adjacent cell is constructed in any one of the four directions: rows, columns and the two diagonal directions, employing wrapping with the extension to the other side of the table when encountering the edge cell, then each row, column and all diagonals, main and wrap, will sum to 0 and every complementary tile, applied to this difference-table will sum to 0 anywhere in the table, including edge-wrapping of the tile pattern !!! This is labeled the zero differential property which holds for all perfect size squares. What this amazing property implies is that these perfect number squares are perfectly balanced; specifically, if a square table were loaded with weights equal to each cell's number, the table would balance if supported underneath by a thin strip across its center in any of the 4 directions. And further, given that the tiles were connected together in a continuous fabric, each tile pattern would resist propagating any ripple effect induced by an impact anywhere beyond one row and column inside the table's border as it otherwise would if it were just floating on water because the inertia of all the surrounding weights would act as a cumulative counter-balancing force in all directions! So the table is planarly stable too. Numeric squares with this level of perfection have never been seen before. All squares of odd-size and even-size divisible by 4 are perfect. Even-size squares not evenly divisible by 4 are only near-perfect (next) and lack these exceptional properties. Near-perfect Numeric Squares
All squares whose size n is two times an an odd-number are only near-perfect. Nonetheless near-perfect squares all possess equal quadrals. At right is a size-6 near-perfect square. It is the first time the size-6 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 amounts ± n/2 when n = 6 and ± (n/2)2 for n > 6. 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 one 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 minimal inequalities in the near-perfect form here so that’s the nearest to perfect status that they come. Beyond this, near-perfect squares possess none of the other amazing properties that perfect squares do. Only when these numeric tables are extended to three dimensions can all the tables be manifested as perfect. All of the foregoing is addressed in the chapter Part II of the book, Number Magic. Matchmaker's "truly magic" squares A brand new kind of numeric 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.
· It has all its diagonals summing to 25, its characteristic number. · Every set of 5 numbers corresponding to a matching of one row to one column, with no row nor column being duplicated nor omitted, sums to 25.
·
There is always only one
row and one column which sum 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 Part VI on matchmaker's squares shows these kinds of squares for sizes 4, 5 and 9; a size-4 cube; and a size-5 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 square is put in normalized form, it is shown to have many of the general properties of the regular square of the first kind even though it has a different range of numbers and a unique set of properties all its own! Now, here is the most amazing result of all the geonomic properties for squares: Every mm-square of prime-number size will generate an ultra-perfect regular square of the same size with all of the properties of regular prime-number size squares, including equal-summing dual tile patterns! Now that's Wow! math. Contrary to the primary premise of Information Theory, here is a table with lesser information that can create a table with more information while the reverse process is impossible! Where is this advance in information coming from? This is the most profound discovery yet. It's on par with the discovery in atomic physics that neutrons and protons are composed of yet smaller particles , called "quarks", existing in even lower dimensions! Here is the single skeleton table underlying both fundamental dual loom tables for prime-number size squares! Now that's even wilder Wow math !!! All this is addressed in chapter Part VI of the book, Number Magic. Absolutely Perfect Magic Cubes 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 rows and planar columns add up to the same number 1575.
·
All the planar levels from
top to bottom add up to the same number 1575 (sum of identically located
rows
·
All the six planar main
diagonals each add up to 1575 (the sum of identically located diagonals
among all · 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. That's now a total of 9 planar slices all adding to the same number simultaneously! (All not shown here.) · The sum of all the numbers in every 5x5 block-square is 1575. · 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) · Both the rows and columns in each block-square sum to 315. · Both main and all wrap diagonals in both directions in each block-square sum to 315.
· The centers of all the block squares sum to 315. · The same "+" and "x" tile patterns in the size-5 squareabove sum to 315 continuously in every block square of the cube. · Each quadral in the central square #3 sums to 252. · Every pair of numbers symmetric with the central pivot sums to 126. · 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. Chapter Part III on cubes in Number Magic book shows perfect cubes for sizes 2 thru 12. All prime-number size cubes are shown to have dual tiling patterns! And furthermore, the center numbers of the individual tiles in each block-square embedded in the cube taken together form a loom table that will generate yet even more perfect cubes! You have to see it to believe it. It can't get any better than this! These cubes are designated as absolutely ultra-perfect.Perfect Magic Hypercubes
The picture below 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
is the common point among all 4
dimensions. The Number Magic book has two chapters on hypercubes, Parts IV and V. Perfect hyper-cubes are shown from size 2 thru 7 in 4-dimensions and from size 2 thru 5 in 5-dim-ensions in very easily observed square and rectangular number arrays.One of the fundamental discoveries revealed in the book is that of the continuous modularity property of 4-dimens-ional tables: Given a 4-dimen-sional table of size n (an n2 by n2 square table) it is shown that every contiguous block-square of size n by n embed-ded anywhere in the table sums to the same characteristic number of the table that do all the cubical rows, columns and diagonals. There are some amazing properties discovered there which uncover what the 4th dimension really looks like!
The primary book Number Magic - The Natural Geometry Hidden in the Natural Number Series describes all these geometries depicted above and depicts all the "magic" tables that can be printed legibly.
This book introduces the reader to the amazing equal-summation patterns of the natural geometry that lie hidden in the natural number series 1, 2, 3 ... . When this continuous stream of numbers is placed in a confined array with geometric boundaries such as a square, cube or hypercube of 4 or more dimensions, amazing equal-summation patterns emerge that are so integrated into each other that it appears as a woven fabric mimicking the boundaries of its confining geometry. This fabric extends beyond the table like a draping table-cloth and can be pulled across the number table either horizontally, vertically or diagonally in either direction and all the while the tile patterns' equalities still persist even though the numbers within them change! And even more surprising is that every perfect magic square of prime-number size has its own unique set of dual complementary characteristic patterns! Below you see the dual complementary tile patterns for the size-17 magic square on one "table".
These complementary tiling patterns found for prime-number size squares are extended to include all perfect squares, cubes and hypercubes. It is demonstrated how these "magic" squares can be woven into equal-summing spatial quilt patterns using loom tables. Loom tables are the fundamental patterns that are the basic patterns underlying perfect magic number tables. These tables come in pairs. Together they not only generate a perfect square, cube or hypercube, but manifest its dual counterpart as well which has all the equal-summation aspects of the first. And this occurs just by interchanging the loom tables' roles in the fundamental manifestation formula. The only thing common about their numbers in these two loom tables are the identical locations of the numbers v0 = 1 and vk = vk-1 + (n+1) for k = 1, 2 … n-1. The locations of all the other numbers are scattered differently. And all these numbers sum to the characteristic number for squares of size n ! The book's Epilogue uses the properties discovered when mapping quadracubes to fathom the actual spatial properties of the 4th dimension. This then results in suggesting that the Einsteinian theory of relativity does not preclude faster than light-speed travel when 4 spatial dimensions are involved! The front cover of the book next depicts the dual loom tables for the perfect size-7 square. Make note of the pattern of numbers: every row, column, diagonal including wrap diagonals, and two distinct tile patterns, each contain the numbers 1 thru n exactly once simultaneously. The Fifth Edition here includes for the very first time my recent discovery of loom tables and their amazing applications. The Fifth Edition is the most extensive work on so-called "magic" number tables in the world.
This basic
discovery of loom tables led to yet another profound discovery: the hidden snowflake
patterns in magic hexagons whose equal summations are the sides of each
nested hexagonal frames symmetrically located about the hexagon's center. Each page in the book is double-side printed in black and white on 8½ by 11 inch pages in large 12pt. lettering. All my books come in a glossy colored soft-cover, perfect-bound publication. The second book shows the various methods that were discovered for manifesting magic squares. It categorizes magic squares into 6 independent classes, each with their own common method of manifestation. The methods yield all the equal-summing patterns mathematically possible for all sizes of squares in each class. These methods are general and apply to any size magic square in its class. You will find this nowhere else unless it has been copyright infringed.
The third book is a derivative of material in the first and includes the latest on modulus table patterns. The Brilliant Number Fabric Woven across Space and Time - Volume I Squares
Synopsis Volume I concentrates solely on squares and leaves higher dimensional number tables to later volumes. This Brilliant Number Fabric - Vol.I book allows one to get introduced to the topic of numeric squares. There's plenty of material there and 99.8% are new patterns never seen before. This volume excerpts from the primary book all of Part II on the basic properties of squares. It is demonstrated that all numeric squares which are perfect possess simultaneous complementary tiling patterns and depicts each from size 5 thru size 31. Recently discovered are the loom tables derived from prime-number size squares. There, the fundamental loom pattern is uncovered upon which 6 basic independent patterns (see cover of second book above) are demonstrated to be woven together across a geometrically-confined space. This subject can no longer be brushed off as mystical curiosities or sacred science because the fundamental weaves have been discovered that integrate every part of 2-dimensional space! Now everything has been discovered for any size numeric square and its all in this one book. The fourth book is also a derivative of the first. The Brilliant Number Fabric Woven across Space and Time - Volume II Cubes
Synopsis
Further, the linear summations both horizontally and
vertically, i.e. channels and pillars, all sum equally. These appeared to be all the planar summations that were possible which sum equally to the the cube's characteristic number until recently when the simultaneous dual tiling patterns found in prime-number size squares were also found in absolutely-perfect cubes too! So it just doesn't get any more dense with equalities than what's presented in this book. The book also shows cubic duality, not addressed in the primary book. The pervasiveness of these equality patterns in every number cube is proof of a brilliant number fabric that wends itself through space and weaves a fabric of equal-summing patterns and has done so throughout time before humans came around to discover them. The modulus and integer loom tables together confirm the pre-existing basic intelligent design patterns of the universe. The fifth book is also a derivative of the first.
The Brilliant Number Fabric
Woven across Space and Time Hypercubes
Volume III excerpts all of Parts IV, V and VI from the primary book. It depicts magic hypercubes from size 2 thru size 7 in 4-dimensions and size 2 thru size 5 in 5-dimensions. All hypercubes including size-2 are shown to be perfect in that all their embedded intersecting cubes and hypercubes are perfect . Further, Volume III shows for the first time what the actual 4th dimension really looks like from a 4-dimensional perspective!The sixth book is a derivative of the first. It is based on Chapter VII in Number Magic. The Atom is a Product of Superior Intelligent Design Here is Mathematical Proof
Synopsis This book develops for the first time ever a plausible basis for the pattern underlying the number of elements in sequential rows of the Periodic Table of Elements, namely the series {2,8,8,18,18,32,32}. Atomic physicists and chemists have yet to offer a fundamental explanation for this particular numeric pattern.
This feat is accomplished
by showing that magic squares and magic cubes hold the answer. The number
and location of octals incident to the characteristic spheres in a series
of perfect cubes are shown to offer a 100% correlation with the
number and orbital paths of electrons in the layered electron-shells of the
noble elements. Then, continuous complementary characteristic tiling
patterns hidden within perfect squares of associated sizes are shown to
provide the missing links needed to explain and account for the number-pairing
of electron-counts between symmetrically-located electron shells in atoms.
This is the first time that such a profound connection between the natural
geometry inherent in the natural number series and the real physical world
has ever been made. 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 can only be the result of a superior intelligent design. Now let me make it clear here that I'm not attempting to provide grist to the creationists who use intelligent design as their camouflage for countering Darwin's theory of evolution. I'm just saying that there are fundamental numerical spatial patterns among the series of natural numbers which can account for the sequence {2,8,8,18,18,32,32} on the right-side of the Periodic Table above that exhibit an undeniable intelligence in their own configuration. That is, there is an underlying numerically complex structure of the atoms that we no less can immediately recognize as being far from random or coincidental. Below is one of the size-17 dual loom tables that underlies the two spherical surface tiling patterns at left and right. The table is duplicated six times to demonstrate the patterns which contain the numbers 1 through 17 exactly once; namely each row, column, diagonal, both main and wrap in both directions, and each characteristic tile pattern throughout the table. That is a complex intricate detailed pattern that is so beyond the mind of Man to concoct; nor is it one that can be derived by classical mathematics! That, my friend, is a pre-existing intelligent design pattern. The Number Magic book shows these dual loom-table patterns for every prime-number-size table from 5 through 31. The simultaneously complementary tile patterns are unique for every size of square.
This is a major discovery in mathematics, never seen before, that is presented for the very first time in my books: The Atom is a Product of Superior Intelligent Design (here), and Number Magic. It has direct application to the quantization of space and is a mathematical demonstration of the quantized vibrations in String Theory to explain the hidden fabric of space.The seventh book, also a derivative of the first, is based on Chapter VIII in Number Magic where hexagons are dealt with. Snowflakes are a Weave of Wonder From the new Wow! math series
This book demonstrates for the first time ever that snowflake patterns are contained in the natural numerical fabric of space itself. It deals with hexagonal geonomic arrangement of numbers 1 thru N = 3n(n-1) + 1 where n is the number of cells along each side and N is the number of cells in the hexagon of size n. It explains how snowflakes form perfect hexagonally symmetric patterns based mostly on the hidden patterns in the fabric of space. Has application to demonstration of the patterns predicted by String Theory in the real world. How to get these books To purchase any of the the Number Magic books listed be low from publisher CreateSpace, click on one of the preferred book title's below. If you wish to order different titles at the same time, click the back arrow after updating your CreateSpace shopping cart to return here. Then just make another selection here and your shopping cart will be automatically updated when you are again transferred back to CreateSpace for a secure transaction.Continue this process until you are ready to complete your shopping and checkout via CreateSpace. All the books in your shopping cart will be delivered together. And unless you select expedited shipping, your order will be delivered to you by FedEx at minimum cost. To order, click on the book's title. Number Magic 338 pages, black & white print the fundamental complete source text -- $24.95 126 pages in black & white print -- $19.95(Based on Parts IIA, IIB, IIC and VI of Number Magic) My only book that shows all the methods of manifesting magic squares that are as perfect as is mathematically possible. The Brilliant Number Fabric Woven Across Space and Time Volume I (Squares), 122 pages, B&W, print(Based on Part II of Number Magic) -- $11.95 The Brilliant Number Fabric Woven Across Space and Time Volume II (Cubes), 70 pages, B&W print(Based on Parts IIB and III of Number Magic) -- $11.95 The Brilliant Number Fabric Woven Across Space and Time Volume III (Hypercubes), 84 pages, B&W print (Based on Parts IV and V of Number Magic) -- $11.95 The Atom is the Product of Superior Intelligent Design: Here's Mathematical Proof. 42 pages in color print (Based on Parts IIC, III and VII of Number Magic) -- $14.95 Snowflakes are a Weave of Wonder 30 pages in color print -- $15.95(Based on Part VIII of Number Magic) Treatment of the Subject 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. Outside of the methods of manifestation, 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 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 5-dimensional quintacube; 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 alone is very enlightening. It contains formulas for calculating the characteristic numbers of every size table in any dimension. It gives formulas relating one type of geometry to any other one in the book. It shows formulas for determining the characteristic number of a given-size number table in going from one dimension to the next. I t is proven in the Appendix, that these number arrangements are pervasive throughout any number of dimensions and are the properties of space and not the properties of the numbers per se'. The Appendix serves well as a teaching guide for demonstrating how patterns are unified under generalized formulations.It is demonstrated throughout the chapters by showing numerous specific examples in a continuous series that multi-dimensional space can be tapped, measured and mapped by two 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 or rectangular 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 throughout in addition to all 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 (See the patterns on the cover for the book, The Atom is a Product of Superior Intelligent Design, below where they are depicted for the size-17 square). They are major fundamental discoveries. For the proof of this claim click here.These equality properties were only discovered recently between January 2005 thru April 2012 through the use of my PC computer employing Microsoft’s Excel program. The tables themselves would enhance the teaching of Excel because of the amazing pervasiveness of the equal-summing patterns. Plus, the amazing properties are all visual. Through the use of two n x n square loom tables that are dual to each other, both derived from the original prime-number size square of size n, the book makes the undeniable case that space itself is quantized within each size confined space with a spatial weave of interwoven strings from 4 different linear directions and within 2 simultaneously-occurring tiling patterns where each contains the numbers 1 thru n exactly once, all simultaneously. These loom tables regenerate the original square as well as generate the original square's dual counterpart, and visa-versa. And it's this double-duality that actually accounts for the pairing of the numbers in the rows of the Periodic Table of Elements. The book explains all this in detail. This is an actual manifestation from the bottom-up of 2-dimensional String Theory. You have to see it for yourself to comprehend it! And it exists nowhere else. About me, the explorer of virtual-space and author 
of these books
I hold Mathematics Degrees from Penn State University (BS 1964) and Stanford University (MS 1971) with a good foundation in the sciences. Just because I don't hold a Ph.D. degree, doesn't imply that I don't know what I am talking about. Further, I don't stutter or use the word "perhaps" over and over again like most academicians do. I am not intimidated by academicians with Ph.D.s. I am affirmative throughout these books because I verified every property that I state as fact. The tables and formulas speek for themselves. 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.Any previously published work on so-called “magic squares“ is so myopic and the field of numerical spatial geometry 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 size squares to surmount the anomalies that occur there for embryonic size tables in 2-dimensions to see the bigger patterns and to get beyond those dimensions into 3-dimensional and 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 some abstruse math journal, but an entire self-published book. This book took retirement and 8 years part-time to write and get it all correct, cross-referenced and coherent. 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 reader with an above-average IQ. I also refrained from using formal terminology that was not really informative and high-sounding although I had to invent some terminology for the many new concepts that have not ever been seen before. The Appendix provides an excellent introduction to practical algebra for K12 students because of all the many pictured patterns are formulated there. There are even more fundamental discoveries in the Appendix where the math is no longer rudimentary. The Appendix shows all the mathematics underlying all these amazing magic number tables for the very first time ever. It's classical in its originality but not yet recognized as classical mathematics that should be taught in schools. It's all new and as such is encountering resistance with educators who in general don't think outside their comfort zone. Unlike tenured academicians, I was not paid for my research by any institution or grant money and consequently I am not under any obligation to give my results and discoveries away without reasonable compensation. The way you get legal access to my work is to purchase my books, CDs or Lecture videos and refrain from duplicating them or presenting the math therein as your own.
DVD in Progress (120 minutes duration with 120 full-color slides)
We are now making a narrated color slide show on DVD of these amazing number patterns and their surprising summation properties, called "The new Wow! Math" series. If you are interested in being on the notification list when these videos become available, please send me an email stating your interest. It's really an easy way to quickly comprehend the Big Picture!Lectures 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 30. Lectures take 1¾ hours plus a 15-minute break. Contact If you wish to contact me, click here: Mr.Math@Live.com . Copyright Notice Every time I come across a numeric square on a website that someone touts as being perfect, I check it with my EXCEL functions for the size square by plopping the numbers as presented into my pre-formulated squares of that size. With the exception of the size-8 square and on only one occasion, the size-5 square, I have never yet found these numeric tables to satisfy all the linear and geometric equal-summing properties for that size that appear in my books here. And for the one incidence of the size-5 square being perfect, it did not possess any tiling patterns. The perfect size 9x9 square which appears in the books on squares is made public there for the very first time. No one has ever produced a perfect size-9 square with all its rows, columns, main and wrap diagonals and all embedded 3x3 block-squares (continuous 3x modularity) each summing to the square's characteristic number, plus having equal quadrals symmetric with the square's center summing to 4/9ths the characteristic number everywhere throughout the square. All perfect and near-perfect magic squares of the same size with all these properties are derivative works of tables in the primary book and these first appeared in the original book Number Magic and were copyrighted there in 2007. The tables and pictures on this page and in these books have been formally copyrighted between 2007 and 2010 and may not be reproduced on other websites, in wikipedia, in presentations, or other publications without written permission by the author or his authorized legal agent. These copyrights will be strictly enforced. Let me make it perfectly clear to academicians right here: Although it be true that one cannot copyright a mathematical formula, these tables of numbers are not formulas, but patterns. These patterns and all their derivatives are copyright-protected by the copyrights already issued. Even though all the mathematical properties of these patterns still hold when the columns or rows are permuted and when the number tables are rotated 90 º, 180º or 270º, all of these are recognized as derivative patterns of the original by the registered copyrights. Be so advised.Intellectual property is the easiest thing to steal because nobody witnesses the immediate theft; it's done by stealth. This material is protected by 10 separate US-issued 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 each edition of the books' publication, any losing defendant will be required by law to pay for all of the author's legal expenses.
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is a property that holds for all odd-size squares but not for all
even-size squares.
Further,
within the 3-dimens-ional cubic blocks are characteristic hemispheres, 1/2
from the primal table and the other 1/2 from its dual table, both
comprising characteristic hyper-spheres in
4-dim-ensional space.
And further yet,
the eight numbers at the corners of every "box" symmetrically located about the
cube's center also sum equally. Not only that, but the numbers at the corners of
all the nested series of octahedrons (8-sided diamonds at right) also sum
equally!
