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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.
Integrate practical insights from modern physics, ancient Hermetic Laws, non-dual meta-physics, transpersonal psychology, and humor, as tools for undoing conflicting beliefs we've dreamed ourselves into. The seven Hermetic laws are explored in depth and demonstrate how a mindfulness that embraces 'other' as 'self' can reverse the typical misapplication of these inescapable laws of Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause & Effect and Generation. Ubiquitous geometric symbols, paired to each of these laws - the circle, vesica piscis, sine wave, line, spiral, fractal and yin-yang - and their countless commonplace variations, seen from the vantage point of shared interests, reflect these ideas. The inspired use of natural law restores attributes of life, love, strength, purity, beauty, perfection and gratitude to our awareness.
Originally published: Presteigne, Powys, Wales: Wooden Books Ltd., 1998.
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.
Looks at the relationship between the five Platonic and thirteen Archimedean solids.
Sacred Geometry is a key to good science, a secret of great art, and a light on the mystical path. The higher dimensional patterns and principles revealed in the Triangles, Hexagons, and Circles of the Flower of Life, attract the human spirit back to its source and accelerate the evolution of consciousness. To truly understand something, means to understand the patterns that create it, and to be able to predict how those patterns unfold. The Flower of Life pattern can be extended as a fractal, containing variations of itself within itself at all scales. It is the template of the fundamental symmetries of form in all the infinite dimensions.This lavishly illustrated little book will entertain and enlighten both beginners and aficionados of the illustrious tradition of Sacred Geometry. It explains the simple logic of the fundamental forms, and delves deeply into the history, philosophy, and mysticism surrounding them. It unveils the source of their attractive power.
The sacred Flower of Life pattern, the primary geometric generator of all physical form, is explored in even more depth in this volume, the second half of the famed Flower of Life workshop. The proportions of the human body, the nuances of human consciousness, the sizes and distances of the stars, planets and moons, even the creations of humankind, are all shown to reflect their origins in this beautiful and divine image. Through an intricate and detailed geometrical mapping, Drunvalo Melchizedek shows how the seemingly simple design of the Flower of Life contains the genesis of our entire third-dimensional existence. From the pyramids and mysteries of Egypt to the new race of Indigo children, Drunvalo presents the sacred geometries of the Reality and the subtle energies that shape our world. We are led through a divinely inspired labyrinth of science and stories, logic and coincidence, on a path of remembering where we come from and the wonder and magic of who we are. Finally, for the first time in print, Drunvalo shares the instructions for the Mer-Ka-Ba meditation, step-by-step techniques for the re-creation of the energy field of the evolved human, which is the key to ascension and the next dimensional world.if done from love, this ancient process of breathing prana opens up for us a world of tantalizing possibility in this dimension, from protective powers to the healing of oneself, of others and even of the planet. Embrace the expanded vision and understanding that Drunvalo offers to the world. Coincidences abound, miracles flourish and the amazing stories of mysteries unveiled arise as the author probes the Ancient Secrets of the Flower of Life.
A beautiful and original book from a renowned thinker and geometrist