EU English Edition

"This book may well turn out to be the most important of its kind in this century."
Keith Critchlow, personal tutor to the family of the Prince of Wales

EU English Edition

"To the modern mind, the prospect of constructing something as immense and intricately detailed as Chartres Cathedral without the use of even a simple school calculator, let alone access to CAD resources that we now use to fabricate the simplest of consumer articles, is incomprehensible. However, anyone versed in the mediaeval education system, will of course know that 4 of the Heptateuchon, or 7 liberal arts, included studies in arithmetic, geometry, astronomy and music.

Charpentier also shows how these mediaeval builders could obtain 'Pi' to 4 decimal places! No mean feat, considering my scientific calculator gives it to only 7 decimal places a mere 900 years later!"

EU English Edition

"Built mostly in the mid- to late fourteenth century atop a hill overlooking Granada, Spain, the Alhambra stands as a stunning example of Moorish architecture, the only Muslim palace to have survived since the Middle Ages. Its inordinate artistic detailing and disorderly layout--"underpinned," Irwin suggests, "by a geometry that [has] mystical resonance"--attract thousands of tourists every day.

In addition, as the site of the Moors' last stand before being driven from Spain by the Christian Reconquista in 1492, it has come to symbolize, for many Arabs and Muslims, everything they have lost in recent centuries."

EU English Edition

"Heath brings the Cosmos back to Earth, demonstrating that the sacred ratios were incorporated into ancient architecture such as Stonehenge and reflected in the musical tones that the ancients sounded to plug into the Divine.

Marks a turning point in the recovery of a whole way of thinking stretching back perhaps tens of thousands of years. A bold and very important contribution to our understanding of our ancestors’ genius."

EU English Edition

"This classic study probes the geometric interrelationships between art and life in discussions that range from Plato, Pythagoras and Archimedes to modern architecture and art, flowers, shells and marine life, the human face and much, much more. Also explored: the Golden Section, geometrical shapes on the plane, geometrical shapes in space, crystal lattices and many other fascinating topics."

EU English Edition

"Examination of shells, leaves, horns, human body, drawings of Leonardo, Leaning Tower of Pisa, etc. 426 illustrations."

EU English Edition

"Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. 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."

EU English Edition

"A comprehensive study of the historic development of division in extreme and mean ratio ("the golden number"), this text traces the concept’s development from its first appearance in Euclid’s Elements through the 18th century. The coherent but rigorous presentation offers clear explanations of DEMR’s historical transmission, poses controversial views on the concept’s relationship to other mathematical topics, and features numerous illustrations."

EU English Edition

"Most readers will have at least dim memories from geometry class of the irrational number pi. Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It is related to phenomena as diverse as the petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins."

EU English Edition

"In this text, 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 Finobacci 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, latice 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."