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The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture

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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 mea 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.


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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 mea 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.

30 review for The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture

  1. 4 out of 5

    زاهي رستم

    ليس من الضروري أن تكون معمارياً.. لتعرف عن النسبة الذهبية، أو ما يسمى الرقم فاي.. والذي يدخل في تصميم كل شيء من حولنا تقريباً.. حتى أنه يدخل في تصميم البشر.. فعلى سبيل المثال.. البعد بين العينين هو عين مضروبة بفاي.. ولكي لا تتشابك الأمور عليك.. ليس من الضروري أن تكون عالم رياضيات لتقرأ عن فاي.. ولكن من الضروري جداً أن تعرف ولو قليلاً عن هذا اللغز.. والذي لم تحل كل أحاجيه بعد. لقد كان لي شرف المشاركة في هذا الكتاب، ولكني لست أدري أكانت المشاركة أم القراءة هي المتعة الأكبر التي سببها لي.. جدير بالقرا ليس من الضروري أن تكون معمارياً.. لتعرف عن النسبة الذهبية، أو ما يسمى الرقم فاي.. والذي يدخل في تصميم كل شيء من حولنا تقريباً.. حتى أنه يدخل في تصميم البشر.. فعلى سبيل المثال.. البعد بين العينين هو عين مضروبة بفاي.. ولكي لا تتشابك الأمور عليك.. ليس من الضروري أن تكون عالم رياضيات لتقرأ عن فاي.. ولكن من الضروري جداً أن تعرف ولو قليلاً عن هذا اللغز.. والذي لم تحل كل أحاجيه بعد. لقد كان لي شرف المشاركة في هذا الكتاب، ولكني لست أدري أكانت المشاركة أم القراءة هي المتعة الأكبر التي سببها لي.. جدير بالقراءة.

  2. 5 out of 5

    Jules

    Beautiful illustration of the intersections between math, music, art, and biology.

  3. 5 out of 5

    Kiel Bryant

    Come for the text; stay for the drawings.

  4. 5 out of 5

    Abrahamus

    I checked this out from the library thinking that I would probably just skim it, but I got so engrossed in it that I read the whole thing. The topic is one of perpetual fascination to me, perhaps bordering on a minor obsession: the pervasiveness of certain geometric patterns and harmonious mathematical relationships all throughout the created order, and most specifically, the relationship known as the golden ratio, or .618…. This unique and remarkable ratio manifests itself virtually everywhere I checked this out from the library thinking that I would probably just skim it, but I got so engrossed in it that I read the whole thing. The topic is one of perpetual fascination to me, perhaps bordering on a minor obsession: the pervasiveness of certain geometric patterns and harmonious mathematical relationships all throughout the created order, and most specifically, the relationship known as the golden ratio, or .618…. This unique and remarkable ratio manifests itself virtually everywhere one turns, in created works of both Divine and human origin: spiral galaxies, hurricanes, sunflowers, the chambered nautilus, the human hand and ear, notable works of architecture and graphic design, ancient Greek pottery, paintings by the likes of DaVinci and Seurat, musical harmonies, and a Boeing 747, all just for starters. No book could possibly be said to cover the topic exhaustively, but this is one of the more thorough treatments I've encountered on the subject. It explores numerous examples of this sort of thing which I had never even begun to consider. There are really fine illustrations and diagrams (many of them quite intricate, detailed and beautiful) on every page. So, in terms of a surface-level analysis of the phenomena, this book is superb. What I find much less satisfying, however, are the author's attempts, interwoven with increasing emphasis as the chapters progress, to discover what this all means on a deeper, spiritual level. Though he never articulates such a position explicitly, it seems that he would probably be on good terms with what has since become the Intelligent Design movement. (This book was originally published in 1981.) As a Christian however, I am firmly convinced that the doctrine of a personal, Trinitarian Deity is the most obvious point of convergence for all the universally imbedded testimonies to intertwined unity and diversity which this book is dedicated to exploring. Though not really surprising, it is nonetheless disappointing to see this conclusion ignored by the author in favor of an unsatisfying and impersonal hodgepodge of eastern dualism, mysticism, and vaguely beneficent evolutionary principles. (That last point is especially a very interesting notion, one which I think would be most difficult to harmonize with Darwin's theory of natural selection.) At any rate, had the author been able to rise above all this, I might have given the book at least four stars.

  5. 5 out of 5

    عُلا

    في العالم الواقعي الذي خلقنا لنطوف به ...ونسعى ...ونعمل ...ونخالط الناس ونصبر على أذاهم ........هناك أنغام جميلة تعيننا على الطريق ....لربما نسمعها بأعيننا أنو نراها بأذاننا أو...أو.... ويا لها من متعة أن نجتمع بها والأروع أن نتعاون معها .......

  6. 5 out of 5

    senä

    This book is the perfect Autonomous Sensory Meridian Response video to me. On numara on yıldız. If I'll ever teach basic design someday, here is my future students' coursebook. The only thing that bothered me a little bit is how the language and author's mindset can go "divine" from time to time, which I rather chose to consider as "poetic". Ignoring that part, this is a beautifully drawn and an eye-opening resource in order to practice ways of seeing, visual proportion, math behind art etc. This book is the perfect Autonomous Sensory Meridian Response video to me. On numara on yıldız. If I'll ever teach basic design someday, here is my future students' coursebook. The only thing that bothered me a little bit is how the language and author's mindset can go "divine" from time to time, which I rather chose to consider as "poetic". Ignoring that part, this is a beautifully drawn and an eye-opening resource in order to practice ways of seeing, visual proportion, math behind art etc.

  7. 4 out of 5

    Chase Lin

    The Power of Limits contains everything we need to know about the hidden formula that governs all of our physical attributes on earth. As a designer and artist, this is a must read book that explains the most fundamental human psychology on the subject of beauty and whatever we may may find comfortable and familiar. It explains the phenomenon of the golden section with in-depth mathematical analysis. Any designer should familiar him/her selves with the law and design accordingly to achieve the c The Power of Limits contains everything we need to know about the hidden formula that governs all of our physical attributes on earth. As a designer and artist, this is a must read book that explains the most fundamental human psychology on the subject of beauty and whatever we may may find comfortable and familiar. It explains the phenomenon of the golden section with in-depth mathematical analysis. Any designer should familiar him/her selves with the law and design accordingly to achieve the connection between their work and anyone who witnesses it. Psychology may have dominated the field of user experience, design, art at this time, but it is mathematics that will carry us to the next stage of the design evolution, and this book will be the bible.

  8. 5 out of 5

    Andrea

    This book shows that great art is proportional with nature. The Egyptians, Greeks, Native Americans, practically everyone knew it as shown in the book -- so why is this news to me? The drawings show how the proportions are based on the Fibonacci series.

  9. 5 out of 5

    *Kashi*

    This is such an interesting book. concerning the Fibonacci sequence, the Golden Ratio, correlation between Music, Art, Architecture and Nature. very Easy to understand and full of Depth and Knowledge.

  10. 4 out of 5

    Susan

    The golden ration in nature. Fascinating.

  11. 5 out of 5

    Pierce Flynn

    Simply amazing and wonderful. This is a "lifelong book to read" that opens deep meaning and natural harmony present in everyday things. This book adds to life! Simply amazing and wonderful. This is a "lifelong book to read" that opens deep meaning and natural harmony present in everyday things. This book adds to life!

  12. 5 out of 5

    Ann

    I love diving into this book to see structures that underly nature, art and architecture, so butterfly wings are like the Parthenona and dolphin skeletons.

  13. 4 out of 5

    Ho

    I LOVE THIS BOOK, YOU CAN GO AS DEEP INTO REALITY AS YOU DESIRE THROUGH THE CONCEPTS IN THIS BOOK.

  14. 4 out of 5

    Liz

    shows mathematics behind nature, golden mean, fractals etc

  15. 5 out of 5

    Paul Brooks

    another great reference book for the student of mathmatics in nature

  16. 5 out of 5

    Miyo

    absolutely fantastic

  17. 5 out of 5

    زاهي رستم

    everything needs math, u will discover that even plants know more than us about math... how, why, we cant know... its a good book.

  18. 5 out of 5

    Romano

  19. 4 out of 5

    Steven Jaycock

  20. 5 out of 5

    Amira Al-shateer

  21. 5 out of 5

    Harsh

  22. 4 out of 5

    Rod

  23. 4 out of 5

    Paul

  24. 5 out of 5

    Ali Schechter

  25. 5 out of 5

    Dejam Freedo

  26. 4 out of 5

    Sunny Shah

  27. 5 out of 5

    Zaker

  28. 4 out of 5

    يحيي احمد

  29. 5 out of 5

    Karen Watson

  30. 5 out of 5

    Jaime Torre Eder

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