Luca Pacioli stood beside the great Leonardo da Vinci and gazed at The Last Supper. He saw immediately that something was terribly wrong. An orphan from a small town in Italy, Pacioli came of age during the Renaissance seemingly destined for a life of struggle and obscurity. But Pacioli had the good fortune of meeting mentors who recognized his uncanny ability with numbers and introduced him to renowned artists and philosophers, royalty, and popes. At a time when many still used Roman numerals and colleges didn’t even teach mathematics, Pacioli was determined to share his passion and make it accessible and understandable. Apprentice to an artist, but a terrible artist himself, he became a master at calculating mathematical perspective in paintings. Tasked with teaching mathematics with no textbook, he wrote his own—followed by books on double-entry bookkeeping, chess, and the divine proportion. In this way, Luca Pacioli, “the father of accounting,” still has something to teach us—not just about mathematics—but about how we account for setbacks in our lives and how we determine what our legacy will be.

Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.

This enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic.

The number Phi, simply defined, is one plus the square root of five, all divided by two. But its myriad occurrences in art, nature, and science have been a source of speculation and wonder for thousands of years. Divine Proportion draws upon both religion and science to tell the story of Phi and to explore its manifestations in such diverse places as the structure of the inner ear, the spiral of a hurricane, the majesty of the Parthenon, and the elusive perfection of the Mona Lisa. A universal key to harmony, regeneration, and balance, Phi is at the heart of a tantalizing story begun on clay tablets in ancient Babylon, and which will continue to be written for centuries to come.

This volume traces W.D. Gann's "Time Factor" and "Law of Vibration" back to the Chaldeans of 3000 BCE Sumer whose principal aspiration was to understand the motion of time. They divided time into years, months, weeks, days, hours, minutes and seconds and devised calendars which helped them predict, and therefore survive, their two rivers' ravaging floods. Inadvertently, their findings also solved the mystery behind the ups and down of money markets. From ancient Sumer to Egypt, ancient China to the native peoples of Central and North America, civilisations unlikely to have had contact with each other built remarkably similar monuments according to geometrical proportions designed to embody cosmic knowledge that would last for all time. Each deciphered time cycles, created calendars and made long term projections of natural phenomena. The Square-of-9 is a matrix embodying nature's cosmic clock. Pauline Novak-Reich takes the reader through ancient math, sacred geometry and lore demonstrating the extraordinary achievements of people who lived in tandem with nature. Each one of these civilisations discovered Nature's "Black Box." Gann often reiterated that: "Everything in existence is based on exact proportion and perfect relationship. There is no chance in nature; because mathematical principles of the highest order lie at the foundation of all things...Vibration is fundamental: nothing is exempt from this law. It is universal, therefore applicable to every class of phenomena on the globe."

Effective visual communication is not an accidental occurrence, but rather is the result of serious intention on the part of the designer to balance all aspects of the design. This is often achieved through careful application of proportion based on guiding principles that are here detailed; the golden ratio, 'divine proportion' and the Fibonacci sequence. By way of 1200 full-colour illustrations, the way in which modern design is utilising these ancient principles is explored.

A series of startling and controversial discoveries reveal a previously unknown mathematical code encrypted in the Bible. The mysterious code was known to Noah and was implemented in the design of the Ark. About 1200 years later, the same code was utilized by Moses, who built the Ark of the Covenant, the Menorah, and the Altar. After another 480 years, the code was embedded into the Temple of Solomon, the decryption of which requires yet another encoded key. A 1000 years passed and the same mysterious code has once again echoed through the parables spoken by Jesus to his disciples. Since then, however, the knowledge of the code appeared to have been completely forgotten. Intriguingly, 1500 years later, during the Renaissance, the ancient "Biblical Code" has once again reappeared, but in the form of musical frequency, and today, is a standard for tuning musical instruments. Moreover, this mystical code serves as an underlying factor or constant for the modern economy and Stock Market. Nonetheless, the roots of this puzzling mystery go even deeper, for it rests within the very fundamental properties of matter and the building blocks of life itself. The question is, "what is the ultimate source of this enigma"?

First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

Human beings are now evolving into a new species, popularized as the light body that starts to grow when our vibration is high enough to activate DNA that exists in our genes. The growing force increases the vibration of all objects over time. When the old body design no longer thrives in the increased vibratory field a species wide metamorphosis triggers. That is where we are today. In early 2006, Mary unexpectedly experienced a kundalini awakening after years of doing meditation. After this, she devoted three years full-time to the kundalini transformation and took daily notes. The core of Our Light Body is Mary's journal for the first year of kundalini transformation with notes, poetry, insights, visions and dreams. The book has chapters with the author's insights about the personality, the higher-self, steps of spiritual awakening, dark nights of the soul, DNA activation, kundalini, human metamorphosis and evolution.

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