Traditional magic squares employ a chessboard-like arrangement of numbers in which the total of all rows, columns, and diagonals add up to the same number. This innovative approach by a Dutch engineer challenges puzzlists to think two dimensionally by replacing numbers with colorful geometric shapes. Dozens of creative puzzles, suitable for ages 12 and up.

As distinct pattern has been found in the apparently infinite, non-recurring decimal of phi, the Living Mathematics of Nature and Biology, the place where the elbow bends in relationship to the whole of the arm. Like Pi, the relationship of the Circle's circumference to its Diameter, mathematicians, for thousands of years, have been obsessed in finding internal patterning in these transcendental numbers. By stepping "In the Next Dimension" Jain has successfully cracked the Phi Code by isolating a recurring pattern that has a distinct periodicity of 24 digits that re-align as 12 Pairs of 9, but it is not vidible nor understandable in Western Maths, online in the Eastern Vedic Mathematics. The latter utilizes a special Sutra or Formula that Digitally Compresses multi-digits to single digits. It also is known as Modulus 9 Maths which is Continued Subtraction of 9 and is the key to the revealed Wheels of 24 that are StarGates. His discover and concept is officially known as the 17th sutra, (a follow on from the incomplete set of 16 tradition vedic mathematics formulae."In The Next Dimension" invites you to view a 2-D circle as a 3D sphere or as a 4D sphere which is a torus doughnut shape. Shape stores Memory, like crystals. The ultimate shape that embodies the Phi Code is the Dodecahedron having 12 pentacle faces, it being the 3D form of the 2D Pentacle. Jain is petitioning for the reintroduction of the Base 12 number system as your original identification and resonance with the measurements of sacred sites like the Pyramids of Egypt and Stonehenge. The Phi Code 108 therefore relates to the 24 edges of the Cuboctahedron: The 12 Spheres Around The Central One.Discover the sequence of Magic Square Constants hidden or encoded in the Tetrahedral Number Series.Jain reveals an original mathematical discover: a better way to define "e" another infinite non-recurring number like Pi and Phi that is the formula for the number of growth and decay in human or bacterial populations.Even if you don't read this book and merely look at the diagrams on almost every page, you will be inspired. Jain believes, through the highly visual content of this material. Any child or adult will be triggered to remember the essential truths captured in the Universal Language of Pictures, Shapes, Numbers and Symbols.

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Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the ''Yu'' square, went on to a life of courtly comfort and fame. Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares--arrays filled with numbers or letters in certain arrangements--held the secret of the universe. Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune. Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization? Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.

A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world. The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.