The Divine Proportion

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.

"... introduces a remarkable new approach to trigonometry and Euclidean geometry, with dramatic implications for mathematics teaching, industrial applications and the direction of mathematical research in geometry" -- p. vii.

Does a mystic, divine formula lie behind everything that is beautiful? For centuries the golden mean has been a subject of endless fascination. The ratio of the proportion can be seen in Nature; it runs through artistic design processes and it affects our perception of our surroundings. But how much of this apparent 'world formula' is true, and how much of it is myth? The history of the golden mean begins with Euclid in the 3rd century BC. But it was only in the 19th century that it was raised to the universal constant of beauty. From this point onwards the 'golden section' was described in flora and fauna; the famous Fibonacci number. It determines the growth of the pineapple; and Le Corbusier optimised architecture by means of the Modulor. But does this art-historical phenomenon really play a universal role in the organisation of our world? Authors from all fields analyse the Golden Mean with regard to function, demonstrability and relevance, also by means of current examples from art and design as well as in comparison with the DIN and the tatami measurement. Exhibition: Museum für Kommunikation, Berlin, Germany (08.09.2016-28.02.2017) / Museum für Kommunikation, rankfurt, Germany (17.03.-27.08.2017). Essays by W. Beinert, A. Beutelspacher, M. Braun, W. Busch, C. Erbar, K. Fendius, J. Fingerhut, H. Fladt, O. Götze, P. Hirschmiller, H. Höge, B. Högner, M.-L. Kinne, M. Kuhn, P. Leins, M. Lauer, D. Lordick, T. Niemeyer, K. Schillinger, F. Schütz, E. Spiekermann, P. Zizka

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.

The elegance of mathematics meets the creativity of art in this unique coloring book. The golden ratio is the mathematical equation that describes what many consider the "divine proportion," and it's found throughout nature, as well as in art and architecture. This stunning coloring book showcases the beauty of Fibonacci's most famous formula, exploring the many ways numbers and beauty combine. Logical and creative minds alike will enjoy filling in the spirals and designs in these remarkable images.

Explores the aesthetic, emotional, artistic and philosophical significance of geometric figures, scientific patterns and mathematical formulas