The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture (Shambhala Pocket Classics)
One of the delights of life is the discovery and rediscovery of patterns of order and beauty in nature—designs revealed by slicing through a head of cabbage or an orange, the forms of shells and butterfly wings. These images are awesome not just for their beauty alone, but because they suggest an order underlying their growth, a harmony existing in nature. What does it mean that such an order exists; how far does it extend?
The Power of Limits was inspired by those simple discoveries of harmony. The author went on to investigate and measure hundreds of patterns—ancient and modern, minute and vast. His discovery, vividly illustrated here, is that certain proportions occur over and over again in all these forms. Patterns are also repeated in how things grow and are made—by the dynamic union of opposites—as demonstrated by the spirals that move in opposite directions in the growth of a plant.
The joining of unity and diversity in the discipline of proportional limitations creates forms that are beautiful to us because they embody the principles of the cosmic order of which we are a part; conversely, the limitlessness of that order is revealed by the strictness of its forms. The author shows how we, as humans, are included in the universal harmony of form, and suggests that the union of complementary opposites may be a way to extend that harmony to the psychological and social realms as well.
All about proportion, pattern, and harmony.
By Ruth Henriquez Lyon - October 23, 2000
For millenia, naturalists and artists have observed repeating geometrical patterns in natural objects. For example, many two- and three- dimensional structures (such as leaves and seashells) have dimensions that reflect the phi ratio, which is (approximately) 1 to 1.618034. This ratio, known amongst the Greeks as the Golden Mean, and used extensively in their sculpture and architecture, lends structural stability, as well as aesthetic balance, to objects into which it is incorporated.
In The Power of Limits, Doczi, an architect, explores some of these basic ratios underlying structures found in the universe-both natural and manmade. He provides beautiful graphics on each page--photographs, drawings, and diagrams, all in black and white. The images illustrate the concepts presented in the text. There is a lot here about dynamic symmetry and Fibonacci number relationships (which gave us the dimensions for the 8 1/2 x 11 inch page and the 3 x 5 index card). But Doczi also... read more
By Kenneth James Michael MacLean - December 28, 2001
This beautifully illustrated and diagrammed book attempts to show the harmony that exists in nature and all good art and architecture. Not only that, Doczi attempts to weave into this picture, (with some success) Pythagorean concepts of harmony and it's relation to growth in nature. The essential concept in this book is the 'power of limits.' Doczi shows that this limiting factor is the golden section. And he does it using almost no math! The golden section has the powerful quality that division or expansion by this proportion always leads to harmonious growth. No matter how small or large is the division, there is never anything "left over" to create disharmony. This limiting factor is of transcendental power, thus "The Power of Limits." Unregulated growth could never achieve anything but randomness, which is not what we observe in nature. Of course in nature and in life it is impossible to achieve perfection. Yet Doczi elegantly explains how... read more
This is the finest book of it's kind
By A Customer - June 30, 1999
Doczi shows the commonality and connectedness of all things in the universe through the perspective of the golden mean. He does so in such a manner that the expert or layman, the physicist or metaphysicist can readily understand. This is by far the most readable book of its kind.
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