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.

A tracing of the history of the concept of the Golden Mean from its prehistoric beginnings through its use by ancient Egyptians and its analysis by the early Greeks. The book chronicles the Golden Mean's use in the Middle Ages and its eventual abandonment after the advent of the Industrial Revolution. The book then demonstrates how the 18th century master gunsmiths applied the Golden Mean and used its unseen, underlying patterns to develop the architectural design for their rifles. A significant idea is the focus on reviving the traditions of the craft and revealing the arts and mysteries of the trade as practiced by these early master gunsmiths of the Kentucky longrifle.

Tells the story of the golden section, a line segment divided into two parts such that the ratio of the short portion to the longer portion is equal to the ratio of the longer portion to the whole, and its impact on civilization and the natural world.

What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.

Don't miss The Pharos Gate, the final volume in the Griffin & Sabine story. Published simultaneously with the 25th-anniversary edition of Griffin & Sabine, the book finally shares what happened to the lovers. Griffin: It's good to get in touch with you at last. Could I have one of your fish postcards? I think you were right—the wine glass has more impact than the cup. –Sabine But Griffin had never met a woman named Sabine. How did she know him? How did she know his artwork? Who is she? Thus begins the strange and intriguing correspondence of Griffin and Sabine. And since each letter must be pulled from its own envelope, the reader has the delightful, forbidden sensation of reading someone else's mail. Griffin & Sabine is like no other illustrated novel: appealing to the poet and artist in everyone and sure to inspire a renaissance in the fine art of letter-writing, it tells an extraordinary story in an extraordinary way.

In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.