Symmetry

1. Front Matter

   Pages i-xi

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2. Introductory chapters

   1. Symmetry, invariance, harmony

      Pages 1-34

   2. Historical Survey

      Pages 35-67

   3. Symmetry in geometrical decorative art

      Pages 69-95

   4. The golden section

      Pages 97-107

3. Interdisciplinary applications

   1. Fibonacci numbers in nature

      Pages 109-130

   2. Perfection and beauty

      Pages 131-169

   3. The mystery of fivefold symmetry

      Pages 171-213

   4. From viruses to fullerene molecules

      Pages 215-241

4. Symmetry in Inanimate Nature

   1. Cosmological symmetries

      Pages 243-253

   2. Sight and Hearing

      Pages 255-270

   3. Symmetries and symmetry breakings in inanimate nature

      Pages 271-316

5. The road from nature to man

   1. Chirality

      Pages 317-349

   2. Cerebral asymmetries

      Pages 351-372

6. Human Creativity

   1. Beauty and truth

      Pages 373-384

   2. Rationality and impression

      Pages 385-414

7. Back Matter

   Pages 415-508

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All of us have a certain conception of what symmetry means, at least as far as its main forms are concerned (like mirror-reflection or rotation, but only rarely translation). What are the common features of these transformations? How can one generalise them to explain similar phenomena that appear in different arts and sciences? What other forms of symmetry can we include in the scope of our study by the application of these generalised rules? How can a common phenomenon lend possible solutions from one discipline to another? Did you know that symmetry is a universal concept that has appeared in all cultures since prehistoric times, accompanying us through the history of mankind? What important role have asymmetries like the one-handedness of the neutrino played in the formation of matter, from the assumed Big Bang through to the asymmetries of the human brain? This book tries to explain these and a number of related questions.
This is the first comprehensive book on the topic since the publication of H. Weyl’s popular book on symmetry more than fifty years ago. It is relevant to almost all fields of science where symmetry appears as a phenomenon or is applied as a method, and where the concept is present in contemporary sciences, humanities and arts.

Symmetry used to be a fundamental phenomenon in crystallography, where its basic concept was elaborated, in morphological biology, and of course in mathematics, which provided its exact description. In the last half century symmetry (and symmetry breaking) has become a leading principle in physics, in all sciences that deal with the structure of matter, as well as in the biochemistry of proteins, the study of the genetic code, brain research (where functional asymmetries have been revealed), psychology, and in developing architectural structures and in business decision-making, to name but a few examples. This book seeks to find common regularities among these apparently disparate phenomena. It coversmost of the achievements reached in the sciences in recent decades that have been given new impetus by the mutual influences of art and science related to symmetry (or the lack of it).

Following two introductory chapters, which include the newest generalisation of the concept of symmetry and outline a historical approach, the author leads the reader, step by step, from the relevant basic phenomena to the most typical applications of different appearances of symmetries in the sciences and the humanities. Several references are made to the history of science and art and to philosophical conclusions. The author avoids unnecessary detail and gives many examples, providing 350 illustrations. The essential knowledge on the topic is arranged in an ontological order, following the self-organisation of matter from investigations into inanimate nature, through the formation of organic matter, to the products of the human mind.

As is demanded by the formulation of the fundamental knowledge for a new discipline, the book keeps to scientific standards. It exceeds the limits of popular science, and is formulated at a university level. Although it presumes the knowledge of an average university student, it avoids difficult mathematical formulations in order to make the subject understandable for adherents of other disciplines.

• Natur
• Symmetry
• architecture
• body
• geometry

From the book reviews:

“This new monograph on Symmetry is warmly recommended to readers either with background in mathematics, science, engineering or humanities, or simply to those who are just interested in a concept overarching and unifying all these disciplines.” (Gábor Gévay, Acta Scientiarum Mathematicarum (Szeged), Vol. 76 (3-4), 2010)

“An accessible semi-popular book aimed at general audience. Indeed, one can find very few mathematical equations throughout the book and instead it abounds with explicit examples and beautiful illustrations. … Many aspects of symmetry are nicely illustrated by hundreds of figures, often using Escher works. This book can serve as an excellent survey of the topic not only for mathematicians, physicists and engineers but also to experts and students in humanities.” (Vojtěch Pravda, Applications of Mathematics, Vol. 54 (4), 2009)

“The author manages it to give a far-reaching insight into this interdisciplinary field … . a very readable and fascinating book which is accessible to nearly everyone, the necessary mathematical background being reduced to a minimum.” (G. Kowol, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)

"This complete and beautifully presented book...relies little on mathematics but offers a bevy of vivid examples and eye catching illustrations...This deep exploration on the fascinating subject of symmetry takes a historical overview. It ranges from the pottery motifs of the misty past to more recent discoveries and applications in particle and high-energy physics, structural and biochemistry chemistry, genetics, brain research, business decision making, and more. The author starts from the very basic definitions of symmetry: reflection, rotation, and translation. From there the mathematical concepts never get beyond anything more complex than Euler's PolyhedralFormula...

Among the liberal excursions into photographic and illustrated examples of symmetry, many are reproduced in full color in a dedicated final section to the book. Other final sections include a long bibliography of related works and indexes by both name and subject. As a result, this book serves not only as enlightening and entertaining reading that can be entered into at any point, but a good reference work on symmetry."—MAA Reviews

• Institute for Research Organization of the Hungarian Academy of Sciences and Symmetrion, Budapest, Hungary

  György Darvas

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