In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons.

    presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.

    What is a tree? Why are they so important to life on Earth? How do they eat, breathe, grow, communicate, and regenerate themselves? How many different kinds of trees are there, and where do they live? In this beautiful little book, illustrated with rare old engravings and specially commissioned drawings, internationally renowned Finnish tree expert Professor Olavi Huikari takes us on an unforgettable journey deep into the secrets of these most majestic of Earth's life forms.

    Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces basic counting systems; significant numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; how numbers affect architecture. Lundy explains why the ideas of Pythagoras still resonate, and she profiles each number from one to ten to show its distinct qualities: why, for example, the golden section is associated with five, and seven with the Virgin Mary.

    These in turn are corresponded to language as musical metaphor. This, in combination with novel graphics and symbols, carries the reader to a basic understanding of melodic, harmonic, and rhythmic principles, as well as Western musical notation. A great primer on music theory for the novice or professional, as well as an invaluable resource for composers and students, it includes the following:- A rich unfolding of metaphors and illustrations to elucidate a notoriously impenetrable and abstract subject.- The properties of the overtone series and how it influences harmonic and melodic thought.- A discussion of epigrams and dialectics exploring how meaning is carried through time.- Rhythm and meter as the marking of time and the organization of it into self-similar structures.- From the circle of fifths to intervals, triads, and later seventh chords and extensions.- How major/minor key tonality and modulation occur, and how they differ from music based upon drones or other types of scales.- How form and structure reflect the relationship of humans to time and emotional states.- A wealth of scales, rhythmic patterns, and notation references in the appendices.

    Harmonograph is an introduction to the evolution of simple harmonic theory, from the discoveries of Pythagoras to diatonic tuning and equal temperament. Beautiful drawings show the octave as triangle, the fifth as pentagram; diagrams show the principles of harmonics, overtones, and the monochord. Anthony Ashton examines the phenomenon of resonance in Chladni patterns, describes how to build a harmonograph of your own, and provides tables of world tuning systems. This inspiring book will appeal to musicians, mathematicians, designers, and artists alike.

    We all dance to these primary rhythms. This book reveals the poetic cosmology that lies within the cycles of the Sun and Moon as seen from the Earth.

    Why are dragons recognised in almost all cultures on Earth? What is the mysterious geomantic gold they secretly guard? The author tells the story of these extraordinary animals through examples drawn from all over the world.

    Harmony is central. There are two key aspects to the visual structure of Islamic design, calligraphy using Arabic script-one of the world's great calligraphic traditions-and abstract ornamentation using a varied but remarkably integrated visual language. This art of pure ornament revolves around two central themes; crystalline geometric patterns, the harmonic and symmetrical subdivision of the plane giving rise to intricately interwoven designs that speak of infinity and the omnipresent center; and idealized plant form, spiraling tendrils, leaves, buds and flowers embodying organic life and rhythm.1. WIDE APPEAL: Anyone interested in science, mathematics, design, architecture, and the natural world.2. AUTHORITATIVE: A compelling blend of scholarship and visual presentation, packs an enormous amount of information into a short space.3. BEAUTIFUL PACKAGE: A bargain at $10.00. Winner of First Prize for Nonfiction at the New York Book Show4. SERIES PURPOSE: All are aimed at bringing ancient wisdom forward into the 21st century.5. INSPIRING: The perfect entrée into a challenging topic; will inspire other reading.

    This gorgeous book features clear, entertaining, and enlightening commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. 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.  With its lush format and layflat dimensions that closely approximate the golden ratio, this is the ultimate coffee table book for math enthusiasts, architects, designers, and fans of sacred geometry.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.From the Hardcover edition.

    Einstein himself said it was “the most valuable theory of my life,” and “of incomparable beauty.” It describes the evolution of the universe, black holes, the behavior of orbiting neutron stars, and why clocks run slower on the surface of the earth than in space. It even suggests the possibility of time travel.And yet when we think of Einstein's breakthrough year, we think instead of 1905, the year of Einstein's Special Theory of Relativity and his equation E=mc2, as his annus mirabilis, even though the Special Theory has a narrower focus.Today the General Theory is overshadowed by these achievements, regarded as 'too difficult' for ordinary mortals to comprehend. In Einstein's Masterwork, John Gribbin puts Einstein's astonishing breakthrough in the context of his life and work, and makes it clear why his greatest year was indeed 1915 and his General Theory his true masterpiece.