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3 More specialized monographs
with some interdisciplinary outlook
 

It is difficult to make strict rules for selecting books of interdisciplinary interest. Sometimes works referring to a concrete discipline still have an interdisciplinary importance. For example, a book on crystallographic symmetry groups is useful not only for crystallographers, but also for people interested in solid state physics, crystalphysics, crystalchemistry, materials science, and, in some cases, even for designers. As a general principle: we consider those books that have some importance outside its primary discipline. Following this principle, we include books related to mathematical- physical topics (e.g., theoretical mechanics, quantum theory, particle physics) although many of these books have a limited target among a group of mathematicians and physicists. We also list books on symmetries in various artistic fields, because these could be useful for artists of other fields and scholars who would like to illustrate scientific books with artistic examples. We also include books on dynamic symmetry in design, a proportion-system proposed by Jay Hambidge on the basis of his studies on Greek art, because we witnessed that some aspects of this topic are also interesting for mathematics students (despite the fact that it has less value for the originally targeted artists and art historians). We also list some old books of historic importance (cf., Section 2.1.1 and the references there). Indeed, we think that dealing with the history of the subject is relevant and advanced students may prepare related reports. Although we also include books written by historians of science on various aspects of symmetry (see Section 3.1), we suggest combining these with the original sources.

What types of books are not included? It is not easy to give strict rules, but here are some general conventions. We do not list books that use the term symmetry or its derivatives
- (1) as a metaphorical expression, e.g.,
* Frye, N. (1947) Fearful Symmetry: A Study of William Blake, Princeton: Princeton University Press, 462 pp. [Here the main title is a quote from Blake's poem].
- (2) as an attribute in a specialized term of a discipline that are rarely used outside a particular field (e.g., symmetric space, symmetric logic).

Note that there are cases where a similar term has great importance in two or more field (e.g., asymmetric synthesis, a chemical process that also attracted the interest of biologists).
 

3.1 History and philosophy of science, cognitive science, psychology, general education
 

Altmann, S. L. (1992) Icons and Symmetries, Oxford: Clarendon Press and New York: Oxford University Press, xii + 104 pp. [History of mathematics and physics; three case-studies: (1) Orsted's paradox of the interaction between the magnetic needle and the electric current; (2) Hamilton's description of rotation by quaternions and the later development of related mathematical tools, (3) symmetry in the classification of energy levels in atoms and solids].

- Spanish trans., Iconos y simetrías, Zaragoza: Prensas Universitarias, 1994, 147 pp.

Burckhardt, J. J. (1988) Die Symmetrie der Kristalle: Von René-Just Haüy zur kristallographischen Schule in Zürich, [The Symmetry of Crystals: From René-Just Haüy to the Crystallographic School in Zurich, in German], Basel: Birkhäuser, 195 pp.

Chakravorty, K. R. (1977) Science Based on Symmetry, Calcutta: Firma KLM, xxi + ca. 500 pp. [Philosophy of science; Indian philosophy, religion, and mysticism].

Hommel, H. (1987) Symmetrie im Spiegel der Antike, [Symmetry as Reflected in the Antiquity, in German], Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-Historische Klasse, Jahrgang 1986, Bericht 5, Hieldelberg: Winter, 59 pp.

Khvan, M. P. (1986) Filosofskoe znachenie printsipa simmetrii v fizike elementarnykh chastits, [Philosophical Meaning of the Symmetry Principle in Particle Physics, in Russian], Moskva: Izdatel'stvo Universiteta druzhba narodov, 199 pp.

Leyton, M. (1992) Symmetry, Causality, Mind, Cambridge, Massachusetts: MIT Press, vii + 630 pp. [Cognitive science; Case studies: perception, liguistics, art, and political prisoners].

Melandri, E. (1974) L'analogia, la proporzione, la simmetria, [Analogy, Proportion, Symmetry, in Italian], Scienze dell'uomo, Vol. 27, Milano: ISEDI, 185 pp. [Logic].

Piersa, H. (1990) Symetria i jej funkcje poznawcze w fizyce, [Symmetry and its Congnitive Functions in Physics, in Polish], Rozprawa habilitacyjna, Lublin, Poland: Wydawnictwo Katolickiego Uniwersytetu Lubelskiego (KUL), 257 pp.

Scholz, E. (1989) Symmetrie, Gruppe, Dualität: Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des 19. Jahrhunderts, [Symmetry, Group, Duality: On the Connection between Theoretical Mathematics and Applications in Crystallography and Structural Design of the 19th Century, in German], Basel: Birkhäuser and Berlin: Deutscher Verlag der Wissenschaften, 406 pp.

Slok, J. et al. (1975) Symmetri i videnskaberne, [Symmetry and the Sciences, in Danish], Det lærde Selskabs publikationsserie, Ny serie, Hæfte 7-8, Aarhus [Denmark]: Universitetsforlaget i Aarhus, 77 pp. [Philosophy of science; note: we include this item because the title-page presents it as a book with multiple authors, although it can be also interpreted as a collection of papers].

Sodnomgombo, D. and Khvan, M. P. (1981) Filosofiya i simmetriya, [Philosophy and Symmetry, in Russian], Ulan Bator, Mongolia: Gosizdat, 206 pp. [Physics].

Tsalikídês, E. G. (1995) Kosmikê armonía kai summetría dia mésou tês klassikês kai eukleídeiou geômetrías, [Cosmic Hamony and Symmetry by Means of Classical and Euclidean Geometry, in Greek], Thessaloníkê [Thessaloniki]: Zêtê, 181 pp. [History of geometry].

Urmantsev, Yu. A. (1974) Simmetriya prirody i priroda simmetrii (Filosofskie i estestvennonauchnye aspekty), [Symmetry of Nature and the Nature of Symmetry (Philosophical and Scientific Aspects), in Russian], Moskva: Mysl', 229 pp. [Philosophy, Biology, System approach].

Van Fraassen, B. C. (1989) Laws and Symmetry, Oxford: Oxford University Press, xv + 395 pp. [Philosophy, Physics]

- French trans., Lois et symétrie, [Series] Mathesis, Paris: Vrin, 1994, 520 pp.

Yaglom [IAglom], I. M. (1988) Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century, Boston: Birkhäuser, vii + 237 pp. [History of mathematics and physics].

Also see
* Khakimov (1986) on philosophy of science ® Section 1.2.6,
* Dienes and Mezard (1971) on logic ® Section 1.2.1.1,
* Horwich (1987) on the philosophical problems of asymmetry in time ® Section 4.3,
and
* the pre-1952 works in the context of history of science ® Section 2.1.1,
* the books on the philosophical aspects of symmetry vs. asymmetry ® Section 4.1.
 

3.2 Exact sciences (mathematics, physics, and chemistry, including mathematical crystallography)
 

3.2.1 General works and popular-scientific books
 

Aneva, B. (1990) Supersimetria: Matematichni metodi na teoretichnata fizika, [Supersymmetry: Mathematical Methods in Theoretical Physics, in Bulgarian], [Series] Lektsii za mladi ucheni, Sofiya [Sofia]: Izdatelstvo na Bulgarskata akademiya na naukite, 82 pp.

Arai, A. (1993) Taishousei no suuri, [The Mathematical Principles of Symmetry, in Japanese], Tokyo: Nihon Hyouronsha, v + 221 pp.

Bandou, M. (1996) Butsuri to taishousei: kuouku kara shinka made, [Physics and Symmetry: From Quarks to Evolution, in Japanese], Tokyo: Maruzen, viii + 182 pp.

Bunch, B. (1989) Reality's Mirror: Exploring the Mathematics of Symmetry, New York: Wiley, xi + 286 pp.

- Japanese trans., Jitsuzai no kagami: Shinmetorii no sekai, [Reality's Mirror: The World of Symmetry, in Japanese], Tokyo: Seidosha, 1994, 350 pp.

Elliott, J. P. and Dawber P. G. (1979) Symmetry in Physics, Vol. 1, Principles and Simple Applications, Vol. 2, Further Applications, London: Macmillan, xix + xviii + 557 pp. [Vol. 1, pp. 1-280; Vol. 2, pp. 281-557]
* Reprint ed., corrected, ibid., 1984. [616 pp. in various pagings].

- Russian trans., Élliot, D. and Dober, P., Simmetriya v fizike, Tom 1, Osnovnye printsipy i prostye prilozheniya, Tom. 2, Dal'neishie prilozheniya, Moskva: Mir, 1983, 364 + 410 pp.

Feynman, R. P. (1997) Six Not-So-Easy Pieces: Einstein's Relativity, Symmetry, and Space-Time, [Originally prepared for publication by R. B. Leighton and M. Sands; New introduction by R. Penrose], Reading, Massachusetts: Addison-Wesley, xxvii + 152 pp.

Gribbin, J. R. (1998) In Search of SUSY: Supersymmetry, String and the Theory of Everything, London: Penguin. [Physics, popular scientific].
* American reprint ed., The Search for Superstrings, Symmetry, and the Theory of Everything, Boston: Little Brown, 1999, x + 212 pp.

Holden, A. (1971) Shapes, Space, and Symmetry, New York: Columbia University Press, viii + 200 pp.
* Reprint ed., New York: Dover, 1991, 200 pp. [Polyhedra].

- French trans., Formes, espace et symétries: Construisez facielement vos solides, [Shapes, Space, and Symmetry: Build Your Solids, in French], [Series] Les Distracts, Paris: Conception, édition, diffusion, information (CEDIC), 1977, 206 pp.

Holod, P. I. and Klimyk, A. U. (1992) Matematychni osnovy teorii symetrii, [Mathematical Foundations of Theory of Symmetry, in Ukrainian], Kiyiv [Kiev]: Naukova dumka, 366 pp.

Icke, V. (1995) The Force of Symmetry, Cambridge [England]: Cambridge University Press, xxi + 338 pp. [Physics, popular scientific].
* Paparback ed., ibid., 1995.

Kompaneets, A. S. (1978) Simmetriya v mikro- i makromire, [Symmetry in the Micro- and the Macro-Worlds, in Russian], Moskva: Nauka, 207 pp. [Popular-scientific].

Mozrzymas, J. (1992) Ewolucja symetrii, [Evolution of Symmetry, in Polish], Wroclaw: Uniwersytet Wroclawski, 96 pp. [Physics].

Pagels, H. R. (1985) Perfect Symmetry: The Search for the Beginning of Time, New York: Simon and Schuster, 390 pp.
* 2nd ed., New York: Bantam, 1991, 390 pp.

- Dutch trans. of the 1st ed., co-author Shilling, G., Volmaakte symmetrie: Speurtocht naar de oorsprong van ruimte en tijd, Amsterdam: Contact, 1988, 432 pp.

- Japanese trans. of the 1st ed., Toki no hajimari e no tabi: Taishousei no butsuri, [Journey to the Beginning of Time: The Physics of Symmetry, in Japanese], Tokyo: Chijin Shokan, 1989, 402 pp.
* Japanese trans. of the 2nd ed., Hoshi kara ginga e: Heesheru no niwa, [From the Stars to the Milky Way: Herschel's Garden, in Japanese], ibid., 1993, 262 pp.

- Portuguese trans. of the 1st ed., Simetria perfeita, Lisboa: Gradiva, 1990, 455 pp.

Raichev, P. P. (1974) Simetriyata na atomniya svyat, [Symmetry of the Atomic World, in Bulgarian], Sofiya [Sofia]: Nauka i izkustvo, 66 pp. [Popular-scientific].

Rychlewski, J. (1991) Symetria przyczyn i skutków, [Symmetry of Causes and Effects, in Polish], Warszawa: Panstwowe Wydawnictwo Naukowe (PWN), 156 pp. [Physics].

Salam, A. (1966) Symmetry Concepts in Modern Physics: Iqbal Memorial Lectures, Lahore, Pakistan: Atomic Energy Centre, 55 pp. [Later the author was awarded the Nobel Prize in Physics for symmetry-related works.]

Schmutzer, E. (1972) Symmetrien und Erhaltungssätze der Physik, [Symmetries and Conservation Laws of Physics, in German], Braunschweig: Vieweg and Berlin: Akademie-Verlag, 165 pp.

- Russian trans., Shmuttser, É., Simmetrii i zakony sokhraneniya v fizike, Moskva: Mir, 1974, 159 pp.

Todorov, I. (1985) Fizika, geometriya, simetriya, [Physics, Geometry, Symmetry, in Bulgarian], Sofiya [Sofia]: Narodna prosveta, 144 pp. [Five lectures given for a broad audience of physicists, mathematicians, and philosophers, 1971-1983].

Verheyen, H. (1996) Symmetry Orbits, Design Science Collection, Boston: Birkhäuser, vi + 236 pp. [Geometry, Crystallography].

Wigner, E. P. (1967) Symmetries and Reflections: Scientific Essays, Bloomington, Indiana: Indiana University Press, viii + 280 pp. [Physics, Philosophy; the author was awarded the Nobel Prize in Physics for symmetry-related works.]
* Reprint ed., Westport, Connecticut: Greenwood Press, 1978, viii + 280 pp.

- Russian trans., enlarged, Vigner, E. P., Étyudi o simmetrii, [Etudes on Symmetry, in Russian], Ed. by Ya. A. Smorodinskii, Moskva: Mir, 1971, 318 pp. [Added part: some related papers by Wigner].

- Hungarian trans, Wigner, J., Szimmetriák és reflexiók, Budapest: Gondolat, 1972, 355 pp. [The initial "J" refers to Jenö (Eugene, in English), which was Wigner's original given name in Hungary].

Yale, P. B. (1968) Geometry and Symmetry, Holden-Day Series in Mathematics, San Francisco: Holden-Day, xi + 288 pp.
* Reprint ed., New York: Dover, 1988.

Zee, A. (1986) Fearful Symmetry: The Search for Beauty in Modern Physics, New York: Macmillan, xiv + 322 pp. [Popular scientific; the main title of the book is a quote from Blake's poem The Tyger (1794); cf., Stewart and Golubitsky (1992) in Section 2.1.2, Reader and Croze (1977) in Section 3.3.1].
* Reprint ed., New York: Collier Books, 1989, xiv + 322 pp.

- Japanese trans., Uchuu no dezain genri: Pariti, geeji, kuouku, [Design Principle of the Universe: Parity, Gauge, Quarks, in Japanese], Tokyo: Hakuyousha, 1989, 438 pp.

- German trans., Magische Symmetrie: Die Ästhetik in der modernen Physik, [Magical Symmetry: The Aesthetics of Modern Physic, in German], Frankfurt am Main: Insel, 1993, 360 pp.

Also see
* the books on history and philosophy of mathematics and physics ® Section 3.1.
 

3.2.2 Structure of matter - atomic or molecular level; applications of group theory
 

Mathematical-crystallographical works on colored symmetry and chemical books on orbital symmetry and the theory of chemical reactions are considered, but kept separately in subsections 3.2.1.1 and 3.2.1.2, respectively.
 

Altmann, S. L. (1991) Band Theory of Solids: An Introduction from the Point of View of Symmetry, Oxford: Clarendon Press and New York: Oxford University Press, xiv + 286 pp.

Alworth, W. L. (1972) Stereochemistry and its Application in Biochemistry: The Relation Between Substrate Symmetry and Biological Stereospecificity, New York: Wiley, xi + 311 pp.

- Spanish trans., Estereoquímica y su aplicación en bioquímica: La relación entre la simetría del sustrato y la estereoespecificidad biológica, Madrid: Alhambra, 1980, xii + 376 pp.

Baggott, J. E. (1994) Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene, Oxford: Oxford University Press., ix + 315 pp. [Buckminsterfullerene = a new form of (carbon) molecules that resemble Buckminster Fuller's dome-structures].
* Paparback ed., ibid., 1996. ix + 315 pp.

- Japanese trans., Kyuukyoku no shinmetorii: Furaaren hakken monogatari, [Ultimate Symmetry: The Story of the Discovery of the Fullerene, in Japanese], Tokyo: Hakuyousha, 1996, 364 pp.

Belger, M. and Ehrenberg, L. (1981) Theorie und Anwendung der Symmetriegruppen, [Theory and Application of Symmetry Groups, in German], Mathematik für Ingenieure, Naturwissenschaftler, Ökonomen und sonstige anwendungsorientierte Berufe, Band 23, Leipzig: Teubner 116 pp.
* 2nd revised ed., ibid., 1988, 116 pp.

Belov, N. V. (1986) Ocherki po strukturnoi kristallografii i fedorovskim gruppam simmetrii, [Studies on Structural Crystallography and Fedorov Groups <Space Groups> of Symmetry, in Russian], Compiled by I. M. Rumanova, G. A. Geguzina, and E. M. Dolivo-Dobrovolskaya, Ed. by E. G. Fesenko, Moskva: Nauka, 278 pp.

Bernal, I., Hamilton, W. C., and Ricci, J. S. (1972) Symmetry: A Stereoscopic Guide for Chemists, San Francisco: Freeman, viii + 180 pp.

Bhagavantam, S. (1966) Crystal Symmetry and Physical Properties, London: Academic Press, x + 230 pp.

Bir, G. L. and Pikus, G. E. (1972) Simmetriya i deformatsionnye effekty v poluprovodnikakh, [in Russian], Moskva: Nauka, 584 pp.

- English trans., Symmetry and Strain-Induced Effects in Semiconductors, [With a foreword by J. C. Hensel], New York: Wiley, 1974, x + 484 pp.

- Polish trans., Symetria i odksztalcenia w polprzewodnikach, [in Polish], Warszawa: Panstwowe Wydawnictwo Naukowe (PWN), 1977, 561 pp.

Birss, R. R. (1964) Symmetry and Magnetism, Series of Monographs on Selected Topics in Solid State Physics, Vol. 3, Amsterdam: North-Holland and New York: Interscience, xx + 252 pp.

Blaizot, J. P. and Toledano, J.-C. (1997) Symétries et physique microscopique, [Symmetries and Microscopical Physics, in French], Paris: Ellipses, xiii + 188 pp.

Boardman, A. D., O'Connor, D. E., and Young, P. A. (1973) Symmetry and its Applications in Science, New York: Wiley, xiii + 305 pp.

Bradley, C. J. and Cracknell, A. P. (1972) The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups, Oxford: Clarendon Press, xii + 745 pp.

- Japanese trans. of a part, Tengun to kuukangun no hyougen, [Representation of Point Groups and Space Groups, in Japanese], Tokyo: Uchida Roukakuho Shinsha, 1975, 361 pp.

Bunker, P. R. (1979) Molecular Symmetry and Spectroscopy, New York: Academic Press, xv + 424 pp.
* 2nd ed., co-author Jensen, P., NRC Research Press, 1998.

- Russian trans. of the 1st ed., Banker, F. R., Simmetriya molekul i molekulyarnaya spektroskopiya, Moskva: Mir, 1981, 451 pp.

Burzlaff, H. and Zimmermann, H. (1977) Kristallographie, Band 1, Symmetrielehre, [Crystallography, Vol. 1, Symmetry-Theory, in German], Stuttgart: Thieme, xii + 275 pp.

Butler, P. H. (1981) Point Group Symmetry Applications: Methods and Tables, New York: Plenum Press, ix + 567 pp.

Carter, R. L. (1998) Molecular Symmetry and Group Theory, New York: Wiley, x + 299 pp.

Cracknell, A. P. (1975) Magnetism in Crystalline Materials: Applications of the Theory of Groups of Cambiant Symmetry, International Series of Monographs in Natural Philosophy, Vol. 72, Oxford: Pergamon Press, vii + 276 pp.

Dmitriev, I. S. (1976) Simmetriya v mire molekul, [in Russian], Leningrad [now Sankt-Peterburg]: Khimiya, 124 pp.

- Czech trans., Dmitrijev, I. S., Symetrie ve svete molekul, Praha [Prague]: Státní nakladatelství technické literatury (SNTL), 119 pp.

- English trans., Revised, Symmetry in the World of Molecules, Moscow: Mir, 1979, 147 pp.

- German trans., Symmetrie in der Welt der Moleküle, Leipzig: Deutscher Verlag für Grundstoffindustrie, 1987, 146 pp.

Donaldson, J. D. and Ross, S. D. (1972) Symmetry and Stereochemistry, New York: Halsted Press Division, Wiley, 234 pp.
* British reprint ed., London: Intertext Books, 1972, 234 pp.

Douglas, B. E. and Hollingsworth, C. A. (1985) Symmetry in Bounding and Spectra: An Introduction, San Diego: Academic Press, xii + 456 pp.

Evarestov, R. A. and Smirnov, V. P. (1993) Site Symmetry in Crystals: Theory and Applications, Springer Series in Solid-State Sciences, Vol. 108, Berlin: Springer, xi + 274 pp.
* 2nd ed., ibid., 1997, xiii + 280 pp.

Ezra, G. S. (1982) Symmetry Properties of Molecules, Lecture Notes in Chemistry, Vol. 28, Berlin: Springer, viii + 202 pp.

Fedorov, E. S. (1949) Simmetriya i struktura kristallov: Osnovnye raboty, [Symmetry and Structure of Crystals: Basic Works, in Russian], Ed. by A. V. Shubnikov and I. I. Shafranovskii, Klassiki nauki [Series], Moskva: Izdatel'stvo Akademii Nauk SSSR, 630 pp. [Basic works of late 19th century, including the discovery of the 230 crystallographic space groups].
- English trans. of the major part of this book in: Fedorov (1971).

Fedorov, E. S. (1971) Symmetry of Crystals, ACA Monograph, No. 7, New York: American Crystallographic Association, x + 315 pp. [Trans. of Fedorov (1949) except the biography and the bibliography of Fedorov; translated by D. Harker and K. Harker].

Fieck, G. (1982) Symmetry of Polycentric Systems: The Polycentric Tensor Algebra for Molecules, Lecture Notes in Physics, Vol. 167, Berlin: Springer, vi + 137 pp.

Flurry, R. L., Jr. (1980) Symmetry Groups: Theory and Chemical Applications, Englewood Cliffs, New Jersey: Prentice-Hall, xii + 356 pp.

- Russian trans., Flarri, R. L., Gruppy simmetrii: Teoriya i khimicheskie prilozheniya, Moskva: Mir, 1983, 395 pp.

Franzen, H. F. (1994) Physical Chemistry of Solids: Basic Principles of Symmetry and Stability of Crystalline Solids, Advanced Series in Physical Chemistry, Vol. 1, Singapore: World Scientific, xiv + 280 pp.

Fricke, H. (1965) Symmetrie als Schlüssel zum Verständnis der organishen Chemie, [Symmetry as a Key for Understanding Organic Chemistry, in German], Praxis-Schriftenreihe, Abteilung Chemie, Band 14, Köln: Aulis, 65 pp.

Fujita, S. (1991) Symmetry and Combinatorial Enumeration in Chemistry, Berlin: Springer, ix + 368 pp.

Griffith, J. S. (1962) The Irreducible Tensor Method for Molecular Symmetry Groups, Prentice-Hall International Series in Chemistry, Englewood Cliffs, New Jersey: Prentice-Hall, 134 pp.

Hall, L. H. (1969) Group Theory and Symmetry in Chemistry, New York: McGraw-Hill, xiii + 370 pp.

Harter, W. G. (1993) Principles of Symmetry, Dynamics, and Spectroscopy, New York: Wiley, xxii + 846 pp.

Hatfield, W. E. and Parker, W. E. (1974) Symmetry in Chemical Bonding and Structure, Colombus, Ohio: Merrill, ix + 277 pp.

Ho, T.-L. (1995) Symmetry: A Basis for Synthesis Design, New York: Wiley, xv + 561 pp. [Chemistry].

Hochstrasser, R. M. (1966) Molecular Aspects of Symmetry, New York: Benjamin, xiii + 355 pp.

- Russian trans., Khokhshtrasser, R., Molekulyarnye aspekty simmetrii, Moskva: Mir, 1968, 384 pp.

Ivchenko, E. L. and Pikus, G. E. (1995) Superlattices and Other Heterostructures: Symmetry and Optical Phenomena, Springer Series in Solid-State Sciences, Vol. 110, Berlin: Springer, xi + 370 pp. [Semiconductors].
* 2nd ed., ibid., 1997, xiii + 382 pp.

Izyumov, Yu. A. and Syromyatnikov, V. N. (1984) Fazovye perekhody i simmetriya kristallov, [in Russian], Moskva: Nauka, 245 pp.

- English trans., enlarged, Phase Transition and Crystal Symmetry, Dordrecht [The Netherlands]: Kluwer, 1990, xx + 443 pp.

Knox, R. S. and Gold, A. (1964) Symmetry in the Solid State, New York: Benjamin, xii + 344 pp.

- Russian trans., Noks, R. and Gold, A., Simmetriya v tverdom tele, Moskva: Mir, 1970, 424 pp.

Kocinski, J. (1983) Theory of Symmetry Changes and Continuous Phase Transitions, Amsterdam: Elsevier, viii + 283 pp.

Ladd, M. F. C. (1989) Symmetry in Molecules and Crystals, Chichester [England]: Ellis Horwood and New York: Halsted Press, 274 pp.

Lax, M. J. (1974) Symmetry Principles in Solid State and Molecular Physics, New York: Wiley, 1974, xi + 499 pp.

Ludwig, W. and Falter, C. (1988) Symmetries in Physics: Group Theory Applied to Physical Problems, Springer Series in Solid-State Sciences, Vol. 64, Berlin: Springer, xi + 461 pp.
* 2nd enlarged ed., ibid., 1996, xiii + 473 pp.

McWeeny, R. (1963) Symmetry: An Introduction to Group Theory and its Applications, The International Encyclopedia of Physical Chemistry and Chemical Physics, Topic 1, Mathematical Techniques, Vol. 3, New York: Macmillan and Oxford: Pergamon Press, xiv + 248 pp.

Mead, C. A. (1974) Symmetry and Chirality, Topics in Current Chemistry, Vol. 49, Berlin: Springer, iv + 88 pp.

Meyer, A. (1981) Symmetriebeziehungen zwischen Kristallstrukturen, Bände 1-2, [Symmetry-Relations between Crystal-Structures, Vols. 1-2, in German], Bochum, Drei-Eck-Verlag, 264 + 164 pp.

Miller, W., Jr. (1972) Symmetry Groups and Their Applications, Pure and Applied Mathematics, Vol. 50, New York: Academic Press, x + 432 pp.

Muck, A. (1987) Symetrie krystalu a vibracní spektra, [Symmmetry of Crystals and Vibrational Spectra, in Czech], Praha [Prague]: Státní nakladatelství technické literatury (SNTL), 266 pp.

- Polish trans., Symetria krysztalów a widma oscylacyjne, Warszawa: Wydawnictwa Naukowo-Techniczne, 1992, 282 pp.

Schonland, D. S. (1965) Molecular Symmetry: An Introduction to Group Theory and its Uses in Chemistry, London: Van Nostrand, xii + 298 pp.

- French trans., La Symétrie moléculaire: Introduction à la théorie des groupes et à ses applications à la chimie, Paris: Gauthiers-Villars, 1971, xii + 336 pp.

Senechal, M. (1990) Crystalline Symmetries: An Informal Mathematical Introduction, Bristol: Hilger, xii + 137 pp.

Slater, J. C. (1965) Symmetry and Energy Bands in Crystals, New York: McGraw-Hill, xii + 563 pp.
* Reprint ed., corrected, New York: Dover, 1972, xii + 563 pp.

Steinborn, D. (1993) Symmetrie und Struktur in der Chemie, [Symmetry and Structure in Chemistry, in German], Weinheim [Germany]: VCH, xv + 435 pp.

Vainshtein, B. K. (1979) Sovremennaya kristallografiya, Tom 1: Simmetriya kristallov, Metody strukturnoi kristallografii, [in Russian], Moskva: Nauka, 383 pp.

- English trans., Modern Crystallography 1: Symmetry of Crystals, Methods of Structural Crystallography, Springer Series in Solid-State Sciences, Vol. 15, Berlin: Springer, 1981, xvii + 399 pp.
* English trans., 2nd enlarged ed., Modern Crystallography 1: Fundamentals of Crystals: Symmetry and Methods of Structural Crystallography, ibid., 1996, xxi + 482 pp.

Veen, A. L. W. E. van der (1911) Physish en kristallografish onderzoek naar de symmetry van diamant, [Physical and Crystallographic Investigation into the Symmetry of Diamond, in Dutch], Leiden: Stijthoff, 58 pp. + 3 stereoscopic tables. [The Dutch spelling is archaic: the modern version of "symmetry" is "symmetrie", etc.].

Zheludev, I. S. (1976) Simmetriya i ee prilozheniya, [Symmetry and its Applications, in Russian], Moskva: Atomizdat, 286 pp.
* 2nd enlarged ed., Moskva: Énergoizdat, 1983, 303 pp.

- Japanese trans. of the 1st ed., Taishousei to sono ouyou, Tokyo: Koudansha, 1979, 303 pp.

Zheludev, I. S. (1987) Fizika kristallov i simmetriya, [Physics of Crystals and Symmetry, in Russian], Moskva: Nauka, 187 pp.

- German trans., Kristallphysik und Symmetrie, Berlin: Akademie-Verlag, 224 pp.

Zhuvikin, G. V. and Hefferlin, R. (1994) Symmetry Principles for Periodic Systems of Molecules, Collegedale, Tennessee: Southern College, 84 pp. + 2 charts.
 

Also see
* Burckhardt (1988) on the history of crystallography ® Section 3.1,
* Scholz, E. (1989) on the history of crystallographic groups ® Section 3.1,
* many textbooks ® Section 1.3.
 

3.2.1.1 Colored symmetry (a mathematical method for describing physical properties of crystals)
 

Jaswon, M. A. and Rose, M. A. (1983) Crystal Symmetry: Theory of Colour Crystallography, Chichester [England]: Ellis Horwood and New York: Halsted Press, 190 pp.

Koptsik, V. A. (1966) Shubnikovskie gruppy: Spravochnik po simmetrii i fizicheskim svoistvam kristallicheskikh struktur, [Shubnikov Groups <Black-and-White Groups>: A Handbook on Symmetries and Physical Properties of Crystal-Structures, in Russian], Moskva: Izdatel'stvo Moskovskogo universiteta, 723 pp.

Loeb, A. L. (1971) Color and Symmetry, Wiley Monographs in Crystallography, New York: Wiley, xiii + 179 pp.
* Reprint ed., Huntington, New York: Krieger, 1978, xiii + 179 pp.

Shubnikov, A. V. (1951) Simmetriya i antisimmetriya konechnykh figur, [Symmetry and Antisymmetry of Finite Figures, in Russian], Moskva: Izdatel'stvo Akademii Nauk SSSR, 172 pp. [Antisymmetry = black-and-white or two-colored symmetry].

- English trans. in: Shubnikov, Belov, et al. (1964).

Shubnikov, A. V., Belov, N. V., et al. (1964) Colored Symmetry, Ed. by W. T. Holser, New York: Macmillan and Oxford: Pergamon Press, xxv + 263 pp. [The first part is the translation of Shubnikov (1951), the second part is based on the works by Belov et al.].

Zamorzaev, A. M. (1976) Teoriya prostoi i kratnoi antisimmetrii, [Theory of Simple and Multiple Antisymmetry, in Russian], Kishinev [Moldavskoi SSR, now Moldova]: Shtiintsa, 283 pp. [Antisymmetry = black-and-white symmetry].

Zamorzaev, A. M., Galyarskii, E. I. and Palistrant, A. F. (1978) Tsvetnaya simmetriya, ee obobshcheniya i prilozheniya, [Colored Symmetry, its Generalizations and Applications, in Russian], Kishinev [Moldavskoi SSR, now Moldova]: Shtiintsa, 275 pp.

Zamorzaev, A. M., Karpova, Yu. S., Lungu, A. P., and Palistrant, A. F. (1986) P-simmetriya i ee dal'neishee razvitie, [P-Symmetry and its Further Development, in Russian], Kishinev [Moldavskoi SSR, now Moldova]: Shtiintsa, 154 pp. [P-symmetry is the generalization of colored symmetry].

Also see
* Kumagai and Sawada (1983) ® Section 1.1.3,
* Dubov et al. (1984-87, Vol. 3) ® Section 1.2.2,
* Zamorzaev and Palistrant (1977) ® Section 1.3,
* Jaskowski (1952) ® Section 2.1.1,
* Shubnikov and Koptsik (1972) ® Section 2.1.2,
* Jablan (1984), Lockwood and Macmillan (1978), Washburn and Crowe (1988) ® Section 2.2.2,
* MacGillavry (1965), Schattschneider (1990) ® Section 2.2.3,
* Vainshtein (1979) ® Section 3.2.2.
Most of these books also present artistic examples (ornamental art, Escher's drawings, etc.). In connection with a fully artistic approach to color and symmetry, without any reference to crystallographic groups, see
* Plehn (1911) ® Section 2.2.3.
 

3.2.1.2 Orbital symmetry and other symmetry principles in the theory of chemical reactions
 

Bellamy, A. J. (1974) An Introduction to Conservation of Orbital Symmetry: A Programmed Text, [Series] Longman Text, London: Longman, x + 77 pp.

- German trans., Lehrprogram Orbitalsymmetrie, [Study-Program Orbital Symmetry, in German], Weinhem [Germany]: Verlag Chemie, 1974, vi + 107 pp.

Entwistle, N. (1972) Orbital Symmetry Correlations in Organic Chemistry: A Guide to the Woodward-Hoffman Rules, New York: Van Nostrand Reinhold, vii + 62 pp.

Gilchrist, T. L. and Storr, R. C. (1972) Organic Reactions and Orbital Symmetry, Cambridge Chemistry Texts, Cambridge [England]: Cambridge University Press, viii + 271 pp.
* 2nd ed., ibid., 1979, vii + 311 pp.

Halevi, E. A. (1992) Orbital Symmetry and Reaction Mechanism: The OCAMS View, Berlin: Springer, xxii + 310 pp. [OCAMS = Optical Correspondence Analysis in Maximum Symmetry].

Lehr, R. E. and Marchand, A. P. (1972) Orbital Symmetry: A Problem-Solving Approach, New York: Academic Press, x + 190 pp.
* British version, London: Academic Press, x + 190 pp.

Orchin, M. and Jaffé, H. H. (1971) Symmetry, Orbitals, and Spectra (S.O.S), New York: Wiley, xiii + 396 pp.

- Japanese trans., Kagaku ketsugouron: Bunshi kidou to taishousei, [Chemical Bound-Rule: Molecule Orbitals and Symmetry, in Japanese], Tokyo: Baifuukan, 1974, 373 pp.

Orchin, M. and Jaffé, H. H. (1971) Supplement for Symmetry, Orbitals, and Spectra: Problems and Answers, [With the help of G. Kuehnlenz and R. Ellis], New York: Wiley, vii + 220 pp.

Pearson, R. G. (1976) Symmetry Rules for Chemical Reactions: Orbital Topology and Elementary Processes, New York: Wiley, ix + 548 pp.

- Russian trans., Pirson, R., Pravila simmetrii v khimicheskikh reaktsiyakh, Moskva: Mir, 1979.

Schipper, P. E. (1994) Symmetry and Topology in Chemical Reactivity, Singapore: World Scientific, xii + 272 pp.

Sunjic, V. (1979) Simetrija granicnih orbitala i reaktivnost u organskoj kemiji, [Symmetry of Limited Orbitals and Reactivity in Organic Chemistry, in Serbo-Croatian], Zagreb: Skolska knjiga, 150 pp.

Woodward, R. B. and Hoffman, R. (1970) The Conservation of Orbital Symmetry, Weinhem [Germany]: Verlag Chemie, 177 pp. [Later both authors were awarded the Nobel Prize in Chemistry for related works.]

- German trans., Die Enthaltung der Orbitalsymmetrie, Weinhem [Germany]: Verlag Chemie, 1972, 177 pp.
 

3.2.3 Structure of matter - subatomic level; applications of mathematical methods in quantum theory and particle physics
 

Coleman, S. (1985) Aspects of Symmetry: Selected Erice Lectures of Sidney Coleman, Cambridge [England]: Cambridge University Press, xiv + 402 pp. [Physics].

Dyson, F. J. (1966) Symmetry Groups in Nuclear and Particle Physics: A Lecture-Note and Reprint Volume, Mathematical Physics Monographs Series, New York: Benjamin, xii + 320 pp. ["Sequel to The Eightfold Way edited by Gell-Mann and Ne'eman"].

Froggatt, C. D. and Nielsen, H. B. (1991) Origins of Symmetries, Singapore: World Scientific, x + 581 pp. [pp. 191-581 reprinted papers]. [Physics].

Lopes, J. L. (1969) Lectures on Symmetry, [Series] Documents on Modern Physics, New York: Gordon and Breach, xi + 170 pp.

Ne'eman, Y. (1979) Symétries jauges et variétés de groupe, [Gauge Symmetries and Group Manifolds, in French], Montréal: Presses de l'Université de Montréal, 141 pp. [Mathematical physics].
 

3.2.4 Astronomy, astrophysics
 

Banhatti, D. G. (1998) Bilateral Symmetry in Active Galaxies, Amsterdam: North-Holland, 182 pp.

Danver, C. G. (1942) A Morphological Investigation of Some Near Galaxies, with Regards to the Lengths and the Form of Their Arms, Their Inclinations and Their Symmetry Properties, Lund [Sweden]: Observatory, 192 pp.

Mozrzymas, J. and Wolanski, A. (1993) Harmonia sfer niebieskich i muzyka abstrakcyjnych symetrii, [The Harmony of Heavenly Spheres and the Music of Abstract Symmetry, in Polish], Wroclaw: Leopoldinum, 1993, 148 pp.
 

3.2.5 Other mathematical-physical questions, applied mathematics
 

3.2.5.1 Geometry and algebra
 

Böhm, J. and Quaisser, E. (1990) Schönheit und Harmonie geometrischer Formen: Sphäroformen und symmetrische Körper, [Beauty and Harmony of Geometrical Figures: Spherical Figures and Symmetric Bodies, in German], Berlin: Akademie-Verlag, 123 + xx pp.

Boltyanskii, V. G. and Vilenkin, N. Ya. (1967) Simmetriya v algebre, [Symmetry in Algebra, in Russian], Moskva: Nauka, 282 pp.

Johnston, B. L. and Richman, F. (1997) Numbers and Symmetry: An Introduction to Algebra, Boca Raton, Florida: CRC Press, 260 pp.

Lander, E. S. (1983) Symmetric Designs: An Algebraic Approach, London Mathematical Society Lecture Note Series, Vol. 74, Cambridge [England]: Cambridge University Press, xii + 306 pp. [Combinatorial configurations].

Miles, R. E. (1995) Symmetric Bends: How to Join Two Lengths of Cord, K & E Series on Knots and Everything, Vol. 8., Singapore: World Scientific, xii + 163 pp. [Mathematical Knot Theory].

Robertson, S. A. (1984) Polytopes and Symmetry, London Mathematical Society Lecture Note Series, Vol. 90, Cambridge [England]: Cambridge University Press, xv + 112 pp. [Polytope = higher dimensional polyhedron].


3.2.5.2 Mathematical analysis, theoretical mechanics, nonlinear mathematics, and related questions
 

Field, M. (1996) Lectures on bifurcation, dynamics and symmetry, Pitman Research Notes in Mathematics, Vol. 356, Harlow: Longman, 159 pp.

Gaeta, G. (1994) Nonlinear Symmetries and Nonlinear Equations, Mathematics and its Applications, Vol. 299, Dordrecht [The Netherlands]: Kluwer, xix + 258 pp.

Garcia, N. M. L. (1985) Simetria e periodicidade, [Symmetry and Periodicity, in Portuguese], Lisboa: ED, v + 214 [Mathematics].

Garrett, R. (1987) Symmetry of Sailing: The Physics of Sailing for Yachtsmen, London: Adlard Coles Nautical, x + 268 pp.
* Paperback ed., ibid., 1995, x + 268 pp.
* American ed., Dobbs Ferry, New York: Sheridan House, 1996, x + 268 pp.

- Italian trans., Fisica della vela: La simmetria tra aerodinamica e idrodinamica nel movimento di un'imbarcazione, [Physics of Sailing: The Symmetry in Aerodynamics and Hydrodynamics in the Movement of a Boat, in Italian], Bologna: Zanichelli, 1990, 416 pp.

Holmes, P., Lumley, J. L., Berkooz, G. (1996) Turbulence, Coherent Structures, Dynamical Systems, and Symmetry, Cambridge Monographs on Mechanics, Cambridge [England]: Cambridge University Press, xviii + 420 pp.

Kavanau, J. L. (1980) Symmetry: An Analytical Tratment, Los Angeles: Science Software Systems, ca. 800 pages in various pagings. [Analytic geometry].

Kavanau, J. L. (1982) Curves and Symmetry, Los Angeles: Science Software Systems. [Analytic geometry].

Marsden, J. E., Montgomery R., and Ratiu, T. (1990) Reduction, Symmetry, and Phases in Mechanics, Memoirs of the American Mathematical Society, No. 436, Providence, Rhode Island: American Mathematical Society, iv + 110 pp.

Mitropolskii, Yu. A. and Lopatin, A. K. (1995) Nonlinear Mechanics, Groups and Symmetry, Mathematics and its Applications, Vol. 319, Dordrecht [The Netherlands]: Kluwer, ix + 377 pp.

Olver, P. J. (1995) Equivalence, Invariants, and Symmetry, Cambridge [England]: Cambridge University Press, xvi + 525 pp. [Mathematical physics].

Sattinger, D. H. (1983) Branching in the Presence of Symmetry, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 40, Philadelphia: Society for Industrial and Applied Mathematics, vii + 73 pp.

Vanderbauwhede, A. (1982) Local Bifurcation and Symmetry, Research Notes in Mathematics, Vol. 75, Boston: Pitman, 350 pp.

Yamashita, J. (1996) Hoteishiki to taishousei, [Equations and Symmetry, in Japanese], [Series] Suugaku a no tabi, Vol. 1, Kyoto: Gendai Suugakusha, 448 pp. [Mathematics].

Also see
* the books on broken symmetry and asymmetry in physics ® Sections 4.1 and 4.3,
* Petukhov (1981) on biomechanics ® Section 3.3.3.
 

3.3 Descriptive sciences (life sciences, earth sciences) and mathematical models in economics, medicine, and technology
 

3.3.1 Life sciences (biology, medicine, and psychology)
 

Charnov, E. L. (1993) Life History of Invariants: Some Explorations of Symmetry in Evolutionary Ecology, Oxford Series in Ecology and Evolution, Oxford: Oxford University Press, xv + 167 pp.

Chubarov, V. A. (1994) Simmetrii litsa i traditsionnaya kitaiskaya meditsina, [Symmetries of the Face and Traditional Chinese Medicine, in Russian], Sankt-Peterburg: Mezhdunarodyi tsentr ekonomiki, nauki i tekhniki, 206 pp.

Dubrov, A. P. (1980) Simmetriya funktsional'nykh protsessov, [Symmetry of Functional Processes, in Russian], Moskva: Znanie, 64 pp. [Biology, Biophysics - with some challenging ideas].

Dubrov, A. P. (1987) Simmetriya bioritmov i reaktivnosti, [in Russian], Moskva: Meditsina.

- English trans., Symmetry of Biorhythms and Reactivity, New York: Gordon and Breach, 1989, ix + 268 pp. [Biology, Biophysics - with some challenging ideas].

Jocobsohn-Lask, L. (1924) Die Kreuzung der Nervenbahnen und die bilaterale Symmetrie des tierischen Körpers, [The Crossing of Neural Pathways and the Bilateral Symmetry of the Animal Body, in German], Abhandlungen aus der Neurologie, Psychiatrie, Psychologie und ihren Grenzgebieten, Heft 26, Berlin: Karger, 125 pp.

Jungnitsch, G. (1984) Vergleichende Untersuchung bei vollsinnigen und geburtsblinden Personen an einer Form der Symmetrietäuschung, [Comparative Study with Fully Sensible and Blind from Birth Persons on a Form of Symmetry-Illusion, in German], Psychologia Universalis, No. 45, Bodenheim [at Frankfurt am Main]: Hain, 1984, 244 pp.

Malakhov, A. A. (1965) L5-simmetriya zhizni, [L5-Symmetry of Life, in Russian], Sverdlovsk [Russia]: Sredne­Ural'skoe knizhnoe izdatel'stvo, 60 pp. [L5-symmetry = 5-fold rotational symmetry].

McCall, J. J. (1997) Search, Symmetry, and Arbitrage: A Unified Approach to the Social and Biological Sciences, Boulder, Colorado: Westview Press.

Reader, J. and Croze, H. (1977) Pyramids of Life: Illuminations of Nature's Fearful Symmetry, Philadelphia: Lippincott, 222 pp. [Zoology, Animal ecology; "fearful symmetry" is a quote from W. Blake's poem The Tyger (1794); cf., Stewart and Golubitsky (1992) in Section 2.1.2, Zee (1986) in Section 3.2.2].
* British ed., Pyramids of Life: An Investigation of Nature's Fearful Symmetry, London: Collins, 1977, 222 pp.

Sukhanov, V. B. (1968) Obshchaya sistema simmetrichnoi lokomotsii nazemnykh pozvonochnykh i osobennosti peredvizheniya nizshikh tetrapod, [in Russian], Leningrad [now Sankt-Peterburg]: Nauka, 227 pp.

- English trans., General System of Symmetrical Locomotion of Terrestrial Vertebrates and Some Features of Movement of Lower Tetrapods, New Delhi: Amerind, [Published for the Smithsonian Institution and the National Science Foundation, Washington, D.C.], 1974, vii + 274 pp.

Sulima, Yu. G. (1970) Biosimmetricheskie i bioritmicheskie yavleniya i priznaki u sel'skohozyaistvennykh rastenii, [Biosymmetrical and Biorhythmical Phenomena and Characteristics of Agricultural Plants, in Russian], Kishinev [Moldavskoi SSR, now Moldova]: Izdatel'stvo Akademii Nauk Moldavskoi SSR, 148 pp.

Also see
* Stewart and Golubitsky (1992) on mathematics and biology ® Section 2.1.2,
* Urmantsev (1974) on philosophy and biology ® Section 3.1,
* Tímár (1979) on Dürer's book on human proportions ® Section 3.4.3,
and
* the books on asymmetry in biology ® Section 4.2.

There is a survey-booklet on symmetry in biology which is shorter than our limit of 50 pages:
* Kasinov, V. B. (1971) O simmetrii v biologii, [On Symmetry in Biology, in Russian], Leningrad [now Sankt-Peterburg]: Nauka, 48 pp.
 

3.3.2 Earth sciences (mineralogy and geology)
 

De Michele, V. (1972) Crystals: Symmetry in the Mineral Kingdom, London: Orbis Books, 80 pp.

Makagonov, E. P. (1991) Simmetriya srostkov mineralnykh individov, [Symmetry of Systems of Single Minerals, in Russian], Moskva: Nauka, 193 pp.

Shafranovskii, I. I. and Plotnikov, L. M. (1975) Simmetriya v geologii, [Symmetry in Geology, in Russian], Leningrad [now Sankt-Peterburg]: Nedra, 144 pp.

Ufimtsev, G. F. (1991) Gornye poiasa kontinentov i simmetriya rel'efa zemli, [Mountain Belts of Continents and Symmetry of the Relief of the Earth, in Russian], Novosibirsk: Nauka, 168 pp.

Yushkin [IUshkin], N. P., Shafranovskii, I. I., and Yanulov [IAnulov], K. P. (1987) Zakony simmetrii v mineralogii, [Laws of Symmetry in Mineralogy, in Russian], Leningrad [now Sankt-Peterburg]: Nauka, 333 pp.
 

3.3.3 Mathematical models in economics, medicine, and technology
 

Bobrowski, L. (1987) Dyskryminacja symetriczna w rozpoznawaniu obrazów: Teoria, algorytmy, zastosowania w komputerowym wspomaganiu diagnostyki medycznej, [Symmetric Discrimination in Recognition of Images: Theory, Algorithms, Application in Computer-Assisted Medical Diagnostics, in Polish], Wroclaw: Ossolineum, 170 pp.

Kholodnyi, V. A. and Price, J. V. (1998) Foreign Exchange Option Symmetry, Singapore: World Scientific, xvii + 134 pp. [Mathematical economics].

Petukhov, S. V. (1981) Biomekhanika, bionika i simmetriya, [Biomechanics, Bionics, and Symmetry, in Russian], Moskva: Nauka, 238 pp.

Sato, R. and Ramachandran, R. V. (1998) Symmetry and Economic Invariance: An Introduction, Research Monographs in Japan-U.S. Business and Economics, Boston: Kluwer, viii + 134 pp. [Mathematical economics].

Tamari, B. (1997) Conservation and Symmetry Laws and Stabilization Programs in Economics, Jerusalem: Ecometry, 58 pp. [Mathematical economics].

Also see the following books that deal with some aspects of symmetry in technology,
* Povileiko (1970) ® Section 1.2.7,
* Grigorovskii (1982) ® Section 1.2.7,
* Shubnikov (1940) ® Section 2.1.1,
* Rohde (1982) ® Section 2.1.2,
* Bérczi (1986-87) ® Section 2.2.3.
 

3.4 Art and the humanities
 

3.4.1 Anthropology
 

Lucich, P. (1987) Genealogical Symmetry: Rational Foundations of Australian Kinship, Armidale, New South Wales: Light Stone Publications, xxxi + 684 pp.

Witherspoon, G. and Peterson, G. (1995) Dynamic Symmetry and Holistic Asymmetry in Navajo and Western Art and Cosmology, American Indian Studies, Vol. 5, New York: Lang, x + 191 pp.

Also see
* the books on pattern analysis ® Sections 2.2.2 and 2.2.3.

In connection with physical anthropology, see
* Tímár (1979) on Dürer's book on human proportions ® Section 3.4.3,
* Schneider (1973) on asymmetry of Greek heads in art ® Section 3.4.3,
* Chubarov (1994) on symmetry of the face and traditional Chinese medicine ® Section 3.3.1,
* Anderson (1897), Mentzer and Friedberg (1983), Starosta (1990) on symmetry and physical education ® Section 3.5.
 

3.4.2 Architecture and design
 

Note that books on Hambidge's dynamic symmetry are listed separately in the subsection 3.4.2.1.
 

Bibliography:
Stocklas, K., ed., (1986) Symmetrie und Asymmetrie in der Architektur, [Symmetry and Asymmetry in Architecture, in German], [Series] IRB-Literaturauslese, Fachbibliographie, No. 1192, Stuttgart: IRB [Informationszentrum Raum und Bau, Fraunhofer Gesellschaft], 64 pp.
* Stocklas, K., ed., 2nd revised ed., ibid., 1989, 40 pp.
* Stocklas, K., ed., 3rd revised ed., ibid., 1992, 54 pp.
* Hezel, D., ed., 4th revised ed., ibid., 1995, 71 pp.
 

Baglivo, J. A. and Graver, J. E. (1983) Incidence and Symmetry in Design and Architecture, Cambridge [England]: Cambridge University Press, xi + 306 pp.

García, S. (1681/1991) Compendio de architectura y simetría de los templos: Conforme a la medida del cuerpo humano, con algunas demostraziones de geometría, año de 1681, [Summary of Architecture and Symmetry of the Temples: In Accordance with the Measurement of the Human Body, with Some Geometrical Demonstrations, Year of 1681, in Spanish], Valladolid: Colegio Oficial de Arquitectos, Vols. 1-2. [Including the facsimile reproduction of Manuscript 8884 of the Biblioteca Nacional, Madrid; here "simetría" means proportion].
* Spanish text ed., Compendio de architectura y simetría de los templos, Salamanca: Hijos de Francisco Nuñez, 1941, 145 pp.
* Mexican text ed., Compendio de arquitectura y simetría de los templos, Churubusco, Mexico: Escuela Nacional de Conservación, Restauración y Museografía, 1979, 650 pp.

Hay, D. R. (1846) First Principles of Symmetrical Beauty, Edinburgh: Blackwood, viii + 88 pp., 100 plates. [Symmetry is "the result of harmonic ratio of numbers"; plane figures the bases of all forms, curvilinear figures; applications: ornamental design, Greek architecture, vases, pottery, etc.].

Kalayan, H. (1988) The Architectural Information through Symmetry, Amman: Department of Antiquities, The Hashimite Kingdom of Jordan, 89 pp.

Kambartel, W. (1972) Symmetrie und Schönheit: Über mögliche Voraussetzungen des neueren Kunstbewusstseins in der Architekturtheorie Claude Perraults, [Symmetry and Beauty: On Possible Prerequisites of the New Artistic Consciousness in the Theory of Architecture of Claude Perrault, in German], München: Fink, 179 pp.

Kask, T. (1971) Symmetrie und Regelmässigkeit: Französische Architektur im "Grand Siècle", [Symmetry and Regularity: French Architecture in the "Grand Siècle", in German], Basel: Birkhäuser, 157 pp.

Kurokawa, M. (1998) Hantaishou no monogaku, [Objects <Objectology, Object-Design> of Antisymmetry <Dissymmetry>, in Japanese], Tokyo: TOTO Shuppan, 162 pp. [The author (p. 54) would like to refer to dissymmetry (the lack of some elements of symmetry), but, unfortunataly, adopts the term hantaishou (antisymmetry), which is an alternative expression for black-and-white symmetry. This usage of hantaishou came from the Japanese translation of the book La Dissymétrie by Caillois (1973), see it in Section 4.1 with an additional note on this problem.]
 
 



 

HYPERTEXTS:

Antisymmetry - Hypertext ® Shubnikov (1951) Section 3.2.1.1.

Note - Hypertext ® Caillois (1973) Japan version, Section 4.1.

HYPERTEXT:

Objectology or Object-Design is our suggested equivalent of Kurakowa's term monogaku or, in other reading, butsugaku. This term is not a well-established in Japanese; it is coming from
mono or butsu = thing, object,
-gaku = learning, study, science, (as suffix) -ology.
Obviously, the term monogaku is broader than product-design and industrial design since objects of fine art and architecture are also considered. This is the reason that we initiate the new expressions objectology or object-design.
 



 

Meunié, L. (1968) L'Architecture et la géométrie: Symétries et rythmes harmoniques, [Architecture and Geometry: Symmetries and Harmonic Rhythms, in French], Paris: Vincent, Fréal, 93 pp.

Ressa A. (1990) Chiese barocche in Piemonte: Nella evoluzione delle figure planimetriche a simmetria centrale, [Baroque Churches in Piemonte: On the Development of the Layout-Figures in Central Symmetry, in Italian], Roma: Quasar, 210 pp.

Ruiz de la Roza, J. A. (1987) Traza y simetría de la arquitectura: En la antigüedad y medievo, [Design and Symmetry of Architecture: In the Antiquity and the Middle Ages, in Spanish], Sevilla: Servicio de Publicaciones de la Universidad, 393 pp.

Smolina, N. I. (1990) Traditsii simmetrii v arkhitekture, [Traditions of Symmetry in Architecture, in Russian], Moskva: Stroiizdat, 343 pp.

Stocklas, K. (1986) - see at the beginning of this section: Bibliography.

Szambien, W. (1986) Symétrie, goût, caractère: Théorie et terminologie de l'architecture à l'âge classique, 1550-1800, [Symmetry, Taste, Character: Theory and Terminology of Architecture in the Age of Classicism, 1550-1800, in French], Paris: Picard, 232 pp.

- Spanish trans., Simetría, gusto, carácter: Teoría y terminología de la arquitectura en la época clásica (1550-1800), Madrid: Akal, 299 pp.

Also see
* Huff, W. S. (1967-77) on basic design ® Section 1.1.3,
* Povileiko, R. P. (1970) on industrial design ® Section 1.2.7,
* Horst (1994) on garden art ® Section 3.4.3.
 

3.4.2.1 Design with dynamic symmetry (a system of proportions
based on square roots of integers)
 

Note that these books represent a method of proportional analysis of art works that are outdated in some sense, but still provide interesting sources not only for some historians of art, but also for educators of mathematics.

Bairati, C. (1952) La simmetria dinamica: Scienza ed arte nell'architettura classica, [Dynamic Symmetry: Science and Art in Classical Architecture, in Italian], Milano: Editrice Poltecnica Tamburini, 100 pp.

Edwards, E. B. (1967) Pattern and Design with Dynamic Symmetry, New York: Dover, xx + 122 pp. [Reprint of the book Dynamarhythmic Design, 1932].

Hambidge, J. (1920) Dynamic Symmetry: The Greek Vase, New Haven, Connecticut: Yale University Press, 161 pp.
* 2nd printing, ibid., 1931, 161 pp.
* Reprint of the original work in a luxury ed., Found Class Reprints.

Hambidge, J. (1923) Dynamic Symmetry in Composition as Used by the Artists, New York: Brentano, 83 pp.
* Reprint ed., ibid., 1927, 83 pp.
* Reprint ed., New Haven, Conn.: Yale University Press, 1948, 83 pp.

Hambidge, J. (1924) The Parthenon and Other Greek Temples: Their Dynamic Symmetry, [With a preface by L. D. Caskey], New Haven, Connecticut: Yale University Press, xxii + 103 pp.

- French trans., Le Parthénon et autres tenples grecs: Leur symétrie dynamique, Marseille: Aurea Carmina, 1995, 130 pp.

Hambidge, J. (1926) The Elements of Dynamic Symmetry, New Haven, Connecticut: Yale University Press and New York: Brentano, xx + 140 pp.
* Reprint ed., New Haven, Conn.: Yale University Press, 1948, xvii + 133 pp.
* Reprint ed., New York: Dover, 1967, xvii + 133 pp.

Hambidge, J. (1932) Practical Applications of Dynamic Symmetry, Ed. by M. C. Hambidge, New Haven, Connecticut: Yale University Press and London: Milford and Oxford University Press, xviii + 109 pp.
* Reprint ed., New Haven, Connecticut: Yale University Press, 1942, xviii + 109 pp.
* Reprint ed., New York: Devin-Adair, 1960, xviii + 109 pp.

Hèmbidzh, D. [Hambidge, J.] (1936) Dinamicheskaya simmetriya v arkhitekture, [Dynamic Symmetry in Architecture, in Russian], Moskva: Izdatel'stvo Vsesoyuznoi akademii arkhitektury, 1936, 202 pp. [Russian translation of some works by J. Hambidge].

Herter, C. (1966) Dynamic Symmetry: A Primer, New York: Norton, xiii + 236 pp.

Knee, K. M. (1988) The Dynamic Symmetry Proportional System is Found in Some Byzantine and Russian Icons of the Fourteenth and Sixteenth Centuries, Redondo Beach, California: Oakwood Publications, 86 leaves.
 

3.4.3 Visual art (painting, sculpture, garden art)
 

Biet, S. (1998) Alexander Calder: Verborgene Symmetrie, [Alexander Calder: Hidden Symmetry, in German], Frankfurt am Main: Fischer, ii + 145 [+ 8] pp. [Calder's mobiles].

Funck-Hellet, C. (1950) Composition et nombre d'or dans les oeuvres peintes de la Renaissance: Proportion, symétrie, symbolisme, [Composition and Golden Number in the Painted Works of the Renaissance: Proportion, Symmetry, Symbolism, in French], Paris: Vincent, Fréal, 111 pp. [Some of the analyses are wayward].

Horst, A. J. van der (1994) Speelse symmetrie in de tuin, [Playful Symmetry in the Garden, in Dutch], Warnsveld, The Netherlands: Terra, 144 pp.

- French trans., Jardins et symétrie, [Gardens and Symmetry, in French], Paris: Abbeville, 1996, 144 pp.

- German trans., Symmetrie im Garten: Spielerischer Umgang mit Gestaltungselementen, [Symmetry in the Garden: Playful Relations with Form-Elements, in German], Hildesheim [Germany]: Gerstenberg, 1996, 144 pp.

Leonard, K. (1988) How to Read a Painting: Lessons in Proportion, Balance and Symmetry, Illustrated by W. Edwards, New Berlin, Wisconsin: Sax Arts and Crafts, 102 pp.

Mohr, M. (1987) Fractured Symmetry: Algorithmische Arbeiten / Algorithmic Works, 1967-1987, [in German and English], Ludwigshafen [Germany]: Wilhelm-Hack-Museum, 119 pp. [Published for an art exhibition].

Scheibler, I. (1960) Die symmetrische Bildform in der frühgriechischen Flächenkunst, [Symmetric Picture-Form in the Early Greek Art of Surface-Decoration, in German], Kallmünz [Germany]: Lassleben, 131 pp.

Schneider, L. A. (1973) Asymmetrie griechischer Köpfe vom 5. Jahrhundert bis zum Hellenismus, [Asymmetry of Greek Heads from the 5th Century [B.C.] to the Hellenism, in German], Stuttgart: Franz Steiner, viii + 168 pp.

Tímár, L. (1979) Albrecht Dürer: Della simmetria dei corpi humani, [in English], Budapest: Chemical Works of Gedeon Richter, 64 pp. [On Dürer's book on human proportions with many illustrations from the 1591 Italian ed. and 1613 French ed.].

- Hungarian version, ibid., 1979.

Also see
* MacGillavry (1965) and Schattschneider (1990) on the graphic art of M. C. Escher ® Section 2.2.3,
* Witherspoon and Peterson (1995) on Navaho painting and its modern adaptation ® Section 3.4.1,
* Kurokawa (1998) on dissymmetry in art ® Section 3.4.2,
and
* the books on dynamic symmetry ® Section 3.4.2.1.
 

3.4.4 Music
 

Hofman-Jablan, J. (1995) Simetrija muzickog dela, [Symmetry of Musical Work, in Serbo-Croatian with an English abstract], Beograd: Zaduzbina Andrejevic, 159 pp.

- English trans., Abbreviated paper version, Visual Mathematics, [Electronic journal], Vol. 1, No. 1, http://www.mi.sanu.ac.yu/vismath/, http://members.tripod.com/vismath/.

Karakulov, B. I. (1989) Symmetriya muzykalnoi sistemy: O melodii, [Symmetry of the Musical System: On the Melody, in Russian], Alma-Ata [Kazakhskoi SSR, now Kazakhstan]: Nauka, 129 pp.

Lendvai, E. (1993) Symmetries of Music: An Introduction to Semantics of Music, Compiled and ed. by M. Szabó and M. Mohay, Kecskemét [Hungary]: Kodály Institute, 155 pp.

- Hungarian trans., Szimmetria a zenében, Kecskemét [Hungary]: Kodály Intézet, 1994, 165 pp.

- German trans., Symmetrien in der Musik: Einführung in die musikalische Semantik, Kecskemét [Hungary]: Kodály Institut and Wien: Universal Edition, 1995, 173 pp.

Massenkeil, G. (1962) Untersuchungen zum Problem der Symmetrie in der Instrumentalmusik W. A. Mozarts, [Studies on the Problem of Symmetry in the Instrumental Music of W. A. Mozart, in German], Stuttgart: Franz Steiner, vii + 145 pp., 106 examples of notes.

Melchert, H. (1994) Symmetrie: Form im Rezitativ der Bachschen Matthäuspassion, [Symmetry: Form in the Recitative of Bach's "St. Matthew Passion", in German], Ed. by R. Schaal, Veröffentlichungen zur Musikforschung, No. 17, Wilhelmshaven [Germany]: Noetzel, 96 pp., 28 examples of notes.

Schröder, H. (1902) Symmetrische Umkehrung in der Musik: Ein Beitrag zur Harmonie- und Kompositionslehre, mit Hinweis auf die hier technisch notwendige Wiedereinführung antiker Tonarten im Style moderner Harmonik, [Symmetrical Inversion in Music: A Contribution to the Study of Harmony- and Composition-Theory with a Reference to the Here Technically Necessary Reintroduction of Ancient Keys in the Style of Modern Harmony, in German], Publikationen der Internationalen Musikgesellschaft, Beihefte, Heft 8, Leipzig: Breitkopf und Härtel, 128 pp.
* Reprint ed., Vaduz [Liechtenstein]: Sändig, 1973, 128 pp.
* Reprint ed., Walluf [at Wiesbaden, Germany]: Sändig, 1973, 128 pp.

Werker, W. (1922) Studien über die Symmetrie im Bau der Fugen und die motivische Zusammengehörigkeit der Präludien und Fugen des "Wohltemperierten Klaviers" von Johann Sebastian Bach, [Studies on the Structural Symmetry in the Fugues and the Motivic Relationship between the Preludes and Fugues in Johann Sebastian Bach's "The Well-Tempered Clavier", in German], Leipzig: Breitkopf und Härtel, vii + 356 pp.
* Reprint ed., ibid., 1969, 356 pp.
* Reprint ed., Vaduz [Liechtenstein]: Sändig, 1984, 354 pp.

Also see
* Goncharenko (1993) ® Section 1.2.8.
 

3.4.5 Literature and linguistics
 

Eggers, H. (1956) Symmetrie und Proportion epischen Erzählens: Studien zur Kunstform Hartmanns von Aue, [Symmetry and Proportion of Epic Short Stories: Studies of Hartmann von Aue's Artistic Form, in German], Stuttgart: Klett, 101 pp.

Étkind, E. G. (1988) Simmetricheskie kompozitsii u Pushkina, [Symmetrical Compositions at Pushkin, in Russian], Parizh [Paris]: Institut d'études slaves, 84 pp.

Gibson, J. M. (1890s-?) The Unity and Symmetry of the Bible, New York: Hodder and Stoughton, viii + 125 pp.
* Microfiche ed., Chicago: American Theological Library Association, 1985.

Fedynyshynets, V. (1989) Symetriya poezii: Khudozhnie oformlennya avtora, [Symmetry of Poetry: Artistic Presentation of the Author, in Ukrainian], Uzhhorod [Ukraine]: Karpaty, 93 pp.

Greenberg, M. (1986) Corneille, Classicism, and the Ruses of Symmetry, Cambridge [England]: Cambridge University Press, xv + 189 pp.

Knight, W. F. J. (1939) Accentual Symmetry in Vergil, Oxford: Blackwell, x + 107 pp.
* Reprint ed., [Series] Garland Library of Latin Poetry, New York: Garland, 1979, x + 107 pp.

Konstan, D. (1994) Sexual Symmetry: Love in the Ancient Novel and Related Genres, Princeton: Princeton University Press, xiii + 270 pp.

Longobardi, G. (1988) Symmetry Principles in the Theory of Syntax, [Series] Quaderni patavini di linguistica, Monografie, 4, Padova, Italy: Unipress, ii + 123 pp.

Montgomery, R. L., Jr. (1961) Symmetry and Sense: The Poetry of Sir Philip Sidney, New York: Greenwood Press, vii + 134 pp.
* Reprint ed., ibid., 1969, vii + 134 pp.

Norrman, R. (1998) Wholeness Restored: Love of Symmetry as a Shaping Froce in the Writings of Henry James, Kurt Vonnegut, Samuel Butler and Raymond Chandler, Frankfurt am Main: Lang, 283 pp.

Schlocker G. (1957) Équilibre et symétrie dans la phrase française moderne, [Equilibrium and Symmetry in Modern French Phrase, in French], Paris: Klincksieck, 124 pp.

Also see
* Markova (1996) ® Section 1.2.8,
* the books on broken symmetry and asymmetry in linguistics, literature, and semiotics ® Section 4.4.
 

3.5 Recreation, games, and sport
 

Anderson, W. G. (1897) Anderson's Physical Education: Health and Strength, Grace and Symmetry, New York: Dana, 102 pp.

Mentzer, M. and Friedberg, A. (1983) Mike Mentzer's Spot Bodybuilding: A Revolutionary New Approach to Body Fitness and Symmetry, New York: Simon and Schuster, 111 pp.

Starosta, W. (1990) Symetria i asymetria ruchów w treningu sportowym, [Symmetry and Asymmetry of Motions in Physical Training, in Polish], Warszawa: Institut Sportu, 320 pp.

Sveton, E. (1989) Symetria: Súbor hier pre deti, mládez a dospelych, [Symmetry: A Set of Games for Children, Youth and Adults, in Slovakian], Bratislava [Czechoslovakia, now Slovakia]: Slovenske pedagogické nakladatelstvo, 281 pp. + 2 attachments. [Board games].

Also see
* Garrett (1987) on the physics of sailing ® Section 3.2.5.2.

There is a booklet on symmetry in chess which is shorter than our limit of 50 pages:
* Zavodny, Z. (1991) Symetrické pescove formace v centru, [Symmetric Pawn Formation in the Center, in Czech], [Series] Sachove strategie, Frydek-Místek [Czechoslovakia, now Czech Republic]: Pliska, 47 pp.



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