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2 Interdisciplinary monographs
and popular-scientific books

2.1 General works with systematic surveys

2.1.1 Pioneering works published until 1952 (when three books appeared independently by Jaskowski, Weyl, and Wolf and Kuhn)

These books have significant historic importance. In addition to these, all of them have materials that are still current. Students may survey them in seminar reports.

Jaeger, F. M. (1917) Lectures on the Principle of Symmetry and its Applications in All Natural Sciences, Amsterdam: Elsevier, xii + 333 pp.
* 2nd enlarged ed., ibid., 1920, xii + 348 pp.

- French trans., Le Principe de symétrie et ses applications, Paris: Gauthier-Villars, 1925, xv + 420 pp.

Jaskowski, S. (1952) O symetrii w zdobnictwie i przyrodzie, [On Symmetry in Decorative Art and Nature, in Polish], Warszawa: Panstwowe Zaklady Wydawnictw Szkolnych, 168 pp.

Niggli, P. (1941) Von der Symmetrie und von den Baugesetzen der Kristalle, [On Symmetry and on the Building-Laws of Crystals, in German], Die Gestalt, Heft 4, Leipzig: Akademische Verlagsgesellschaft, 64 pp.

Nicolle, J. (1950) La Symétrie et ses applications, [Symmetry and its Applications, in French], [With a preface by L. de Broglie], Paris: Michel, 182 pp.

- German trans., Die Symmetrie und ihre Anwendungen, Berlin: Deutscher Verlag der Wissenschaften, 1954, 172 pp.

Shubnikov, A. V. (1940) Simmetriya (Zakony simmetrii i ih primenenie v nauke, tekhnike i prikladnom iskusstve), [Symmetry (The Laws of Symmetry and Their Application in Science, Technology, and Applied Art), in Russian], Moskva: Izdatel'stvo Akademii Nauk SSSR, 176 pp. [Cf., Shubnikov and Koptsik (1972) in Section 2.1.2, which is published as the 2nd enlarged ed. of this; however, the volume of that book is about twice larger than this one, and thus we suggest to consider it as a separate item].

Vul'f [Wulff], G. V. (1908) Simmetriya i ee proyavleniya v prirode, [Symmetry and its Manifestations in Nature, in Russian], Moskva: Sytin, 134 pp.
* 2nd ed., Moskva: Izdatel'skii otdel narodnogo komissariata prosveshcheniya, 1919, 135 pp.
* Reprint ed., In: Vulf', Yu. [sic] V., Izbrannye raboty po kristallofizike i kristallografii, [Selected Works on Crystalphysics and Crystallography, in Russian], Moskva: Gosudarstvennoe izdatel'stvo tekhniko-teoreticheskoi literatury, 1952, 242-320. [Note that the author's first name was used in two different versions: Georgii and Yurii].

Weyl, H. (1952) Symmetry, Princeton, New Jersey: Princeton University Press, 168 pp. [Based on a series of lectures given for a broad audience].
* Reprint and paperback eds., ibid., 168 pp.

- German trans. [authorized by Weyl], Symmetrie, [Series] Wissenschaft und Kultur, Band 11, [With a new preface by Weyl], Basel: Birkhäuser, 1955, 157 pp.
* German trans., 2nd ed., ibid., 1981, 157 pp.

- Japanese trans., Shinmetorii: Bi to seimei no bunpou, [Symmetry: The Grammar of Beauty and Life, in Japanese], Tokyo: Kinokuniya Shoten, 1957, ii + 165 pp. [With a commentary by H. Touyama, pp. 159-165].
* Japanese reprint ed., Shinmetorii, ibid., 1970, ii + 165 pp. [The earlier subtitle is not used; H. Touyama's commentary is revised, pp. 159-165].
* Japanese reprint eds. of the latter, ibid.

- Spanish trans., La Simetría, [Series] Colección Interciencia, 5, Buenos Aires: Nueva Vision, 1958, 132 pp.
* Spanish trans., other version, La Simetría, Barcelona: Promoción Cultural, 1974. [With an introduction by E. Bonet].
* Spanish trans., other version, Simetría, Madrid: McGraw-Hill, 1990, x + 130 pp.

- Polish trans., Symetria, Warszawa: Panstwowe Wydawnictwo Naukowe (PWN), 1960, 202 pp.
* Polish trans., 2nd corrected ed., Symetria, Klasycy Nauki [Series: Classics of Science], Warszawa: Prószynski i S-ka, 1997, 157 pp.

- Italian trans., La simmetria, Milano: Feltrinelli, 1962, 175 pp.
* Italian trans., 2nd ed., ibid., 1981, 173 pp.

- French trans., Symétrie et mathématique moderne, [Symmetry and Modern Mathematics, in French], Paris: Flammarion, 1964, 151 pp.
* French reprint eds., ibid.

- Rumanian trans., Simetria, Bucuresti: Editura Stiintifica, 1966, 184 pp.

- Russian trans., Veil', G., Simmetriya, Ed. by B. A. Rozenfel'd, Moskva: Nauka, 1968, 190 pp. [With a commentary by the editor, pp. 168-173, and two additonal articles in Russian: "Weyl and the concept of symmetry" by I. M. Yaglom [IAglom], pp. 5-32, and "Weyl and the metodological problems of science" by B. V. Biryukov, pp. 174-190; the cover design is based on M. C. Escher's Lizards].

- Bulgarian trans., Vail, Kh., Simetriya, Sofiya [Sofia]: Nauka i izkustvo, 1969, 215 pp. [Translated from English; additional materials translated from the Russian ed.: a part of the commentary, pp. 167-169, and I. M. Yaglom's article, pp. 170-215].

- Hungarian trans., Szimmetria, Budapest: Gondolat, 1982, 226 pp. [With additonal articles by T. Nagy (physics), J. Kiss (biology), S. Bérczi (phyllotaxis, polyhedra), respectively].

- Chinese trans., Duìchèn, Beijing [Peking]: Shangwù, 1986, 116 pp.
* Chinese trans., other version, Duìchèn: Meide kexué chanshù, [Symmetry: Explaining the Beauty of Science, in Chinese], Táibei [Taipei, Taiwan]: Zhèngzhong, 1988, 151 pp.
* Chinese trans., other version, Duìchènxìng, Shanghai: Shanghai fanyì chuban gongsi, 1991, vi + 156 pp.

- Greek trans., Summetría, Athêna [Athens]: Trohalía, 1991, 188 pp.

Wolf, K. L. and Kuhn, D. (1952) Gestalt und Symmetrie: Eine Systematik der symmetrischen Körper, [Gestalt and Symmetry: A Systematic Presentation of Symmetric Bodies, in German], Tübingen: Niemeyer, 64 pp.

- Spanish trans., Forma y simetría: Una sistemática de los cuerpos simétricos, Buenos Aires: Editorial Universitaria de Buenos Aires, 1977, 55 pp.

Also see the following pre-1952 books:
* Shepard (1948) on pattern analysis ® Section 2.2.2,
* Plehn (1911) on colored patterns ® Section 2.2.3,
* Veen (1911) on the diamond ® Section 3.2.2,
* Danver (1942) on astronomy ® Section 3.2.4,
* Jocobsohn-Lask (1924) on biology ® Section 3.3.1,
* Hay (1846) on basic design ® Section 3.4.2,
* Schröder (1902) and Werker (1922) on music ® Section 3.4.4,
* Anderson (1897) on physical education ® Section 3.5,
* Gauze (1940) on asymmetry of the protoplasm ® Section 4.2,
* Lautman (1946) on mathematical and physical symmetry and dissymetry ® Section 4.3.

Also see the modern editions of classical works:
* Fedorov (1949), Fedorov (1971) on symmetry groups (collections of late 19th century works in Russian and in English, respectively) ® Section 3.2.2,
* García, S. (1681/1991) on architecture ® Section 3.4.2,
* Tímár (1979) on Dürer's book on human proportions ® Section 3.4.3.

2.1.2 Works published after 1952

Alsina i Català, C. [Alsina Catalá, C.] and Fortuny, J. M. (1988) Fascinant simetria, [Fascinating Symmetry, in Catalan], Barcelona: Fundació Caixa de Pensions, 71 pp. [Published for an exhibition at the Museu de la Ciència (Science Museum) in Barcelona].

- Spanish trans., Fascinante simetría, [Fascinating Symmetry, in Spanish], Barcelona: Fundación Caja de Pensiones, 1990, 71 pp.

Genz, H. (1987) Symmetrie - Bauplan der Natur, [Symmetry: Blueprint of Nature, in German], München: Piper, 464 pp.
* 2nd revised ed., ibid., 1992, 464 pp.

Hahn, W. (1989) Symmetrie als Entwicklungsprinzip in Natur und Kunst, [in German with an English summary], [With a preface by R. Riedl], Königstein [Germany]: Langewiesche, 320 pp. [Very many illustrations, including some color plates].

- English trans., enlarged, Symmetry as a Developmental Principle in Nature and Art, Singpore: World Scientific, 1998, xxi + 510 pp.

Hargittai, I. (1983) Szimmetria egy kémikus szemével, [in Hungarian], Budapest: Akadémiai Kiadó, 292 pp.

- English trans., enlarged, co-author Hargittai, M., Symmetry through the Eyes of a Chemist, Weinheim [Germany]: VCH, 1986, xii + 458 pp.
* Emglish paperback ed., New York: VCH, 1987.
* English trans., 2nd ed., New York: Plenum Press, 1995, xii + 469 pp.

- Russian trans. of the first English ed., Simmetriya glazami khimika, Moscow: Mir, 1989, 494 pp.

Hargittai, I. and Hargittai, M. (1994) Symmetry: A Unifying Concept, Bolinas, California: Shelter Publications, xviii + 222 pp. [Many photographic illustrations].
* Reprint ed., ibid., 1996, xviii + 222 pp.

- German trans. Symmetrie: Eine neue Art die Welt zu Sehen, [Symmetry: A New Way to See the World, in German], Rowohlt Taschenbuch, 1998.

Hargittai, M. and Hargittai, I. (1989) Fedezzük föl a szimmetriát!, [Discover Symmetry!, in Hungarian], Budapest: Tankönyvkiadó, 148 pp. [Popular-scientific, also for children].

- Swedish trans., Upptäck symmetri!, Stockholm: Natur och Kultur, 1998, 144 pp.

Heilbronner, E. and Dunitz, J. (1992) Reflections on Symmetry: In Chemistry ... and Elsewhere, Weinheim [Germany]: VCH and Basel: Helvetica Chimica Acta, vi + 154 pp.

Lisicky, M. (1980) Zivá symetria, [Living Symmetry, in Slovakian], Bratislava [Czechoslovakia, now Slovakia]: Mladé letá. [Popular-scientific, for children].

Mainzer, K. (1988) Symmetrien der Natur: Ein Handbuch zur Natur- und Wissenschaftsphilosophie, Berlin: de Gruyter, xii + 739 pp.

- English trans., Symmetries of Nature: A Handbook for Philosophy of Nature and Science, Berlin: de Gruyter, xiii + 681 pp.

Morita, M. (1980) Taishousei genri: Busshitsu to uchuu o shihaisuru migi to hidari, [Symmetry Theory: Matter and Universe Ruled by Right and Left, in Japanese], [Series] Blue Backs / Buruu bakkusu, B-420, Tokyo: Koudansha, 228 pp. [Popular-scientific].

Merle, P. (1955) L'Homme, le rythme et la symétrie, [The Human, the Rhythm and the Symmetry, in French], Paris: Expansion scientifique française, 254 pp.

Nicolle, J. (1955) La Symétrie dans la nature et les travaux des hommes, [Symmetry in Nature and the Works of Humans, in French], [With a preface by L. de Broglie], Paris: La Colombe, 136 pp.

Nicolle, J. (1957) La Symétrie, [Symmetry, in French], Que sais-je?, Le Point des connasissances actuelles, No. 743, Paris: Presses Universitaires de France, 116 pp.
* 2nd ed., ibid., 1965, 128 pp. [Popular-scientific].

- Spanish trans., Simetría, Buenos Aires: Fabril.

Rohde, G. M. (1982) Simetria: generalidades sôbre simetria, geociências, biociências, ciências exatas, tecnologias e artes, filosofia, [Symmetry: Generalities Concerning Symmetry - Geosciences, Biosciences, Exact Sciences, Technics and Arts, Philosophy, in Portuguese], Sao Paulo: Hemus, 191 pp.

Roman, T. (1963) Simetria - prezentare matematica a unor fenomene din natura si arta, [Symmetry - Presenting the Mathematics of Certain Phenomena in Nature and Art, in Rumanian], Bucuresti: Technica, 254 pp.

Rosen, J. (1975) Symmetry Discovered: Concepts and Applications in Nature and Science, Cambridge [England]: Cambridge University Press, xi + 138 pp.
* Reprint ed., corrected, Mineola, New York: Dover, 1998, xiv + 152 pp.

- Japanese trans., Shinmetorii o motomete, Tokyo: Kinokuniya Shoten, 1977, 182 pp.

Rosen, J. (1983) Symmetry Primer for Scientists, New York: Wiley, xiv + 192 pp.

Rosen, J. (1995) Symmetry in Science: An Introduction to the General Theory, New York: Springer, xv + 213 pp.

Shafranovskii, I. I. (1968) Simmetriya v prirode, [Symmetry in Nature, in Russian], Leningrad [now Sankt-Peterburg]: Nedra, 184 pp.
* 2nd revised ed., ibid., 1985, 167 pp.

Sheikov, N. (1977) Zhivot i simetriya, [Life and symmetry, in Bulgarian], [Series] Biblioteka radar, Sofiya [Sofia]: Narodna mladezh, 169 pp.
* 2nd ed., ibid., 1986, 160 pp. [Popular-scientific].

- German trans., abridged and revised, Scheikov, N., Leben und Symmetrie, [Series] Akzent, Leipzig: Urania, 1982, 128 pp.

- Hungarian trans. of the German version, Sejkov, N., Élet és szimmetria, [Series] Gondolta zsebkönyvek, Budapest: Gondolat, 1987, 127 pp.

Shubnikov, A. V. and Koptsik, V. A. (1972) Simmetriya v nauke i iskusstve, [in Russian], Moskva: Nauka, 339 pp. [Cf., Shubnikov (1940) in 2.1.1 and the note there].

- English trans., Symmetry in Science and Art, New York: Plenum Press, 1974, xxv + 420 pp.

Stewart, I. and Golubitsky, M. (1992) Fearful Symmetry: Is God a Geometer?, Oxford: Blackwell, xix + 287 pp. [The main title of the book is a quote from W. Blake's poem The Tyger (1794); cf., Zee (1986) in Section 3.2.1, Reader and Croze (1977) in Section 3.3.1].

- German trans., Denkt Gott Symmetrisch?: Das Ebenmass in Mathmematik und Natur, [Does God Think Symmetrically: Symmetry in Mathematics and Nature, in German], Basel: Birkhäuser, 1993, 302 pp.

- Italian trans., Terribili simmetrie: Dio e un geometra?, [Terrible Symmetries: Is God a Geometer?, in Italian], Torino: Bollati Boringhieri, 1995, 341 pp.

- Japanese trans., Taishousei no yabure ga sekai o tsukuru: Kami wa kikagaku o aishita ka, [The Breaking of Symmetry Creates the World: Does God Love Geometry?, in Japanese], Tokyo: Hakuyousha, 1995, 346 pp.

- Spanish trans., ¿Es Dios un geómetra? Las simetrías de la naturaleza, [Is God a Geometer? The Symmetries of Nature, in Spanish], Barceolona: Crítica, 1995, 311 pp.

Tarasov, L. V. (1982) Étot udivitel'no simmetrichnyi mir: Posobie dlya uchashchikhsya, [This Amazingly Symmetric World: Book for Pupils, in Russian], Moskva: Prosveshchenie, 176 pp. [Popular-scientific].

- English trans., This Amazingly Symmetric World, Moscow: Mir, 1986, 164 pp.

- German trans., Tarassow, L., Symmetrie, Symmetrie!: Strukturprinzipien in Natur und Technik, [Symmetry, Symmetry!: Structure-Principles in Nature and Technology, in German], Heidelberg: Spektrum, 1993, 235 pp.

Wade, D. (1993) Crystal and Dragon: The Cosmic Dance of Symmetry and Chaos in Nature, Art and Consciousness, Rochester, Vermont: Destiny Books, 287 pp.
* British version [with no reference to symmetry], Crystal and Dragon: The Cosmic Two-Step, Bideford [England]: Green Books, 1991, 287 pp.

Wolf, K. L. and Wolff, R. (1956) Symmetrie: Versuch einer Anweisung zu gestalthaftem Sehen und sinnvollem Gestalten, systematisch dargestellt und an zahlreichen Beispielen erläutert, 1. Textband, 2. Tafelband, [Symmetry: An Attempt towards an Instruction in Seeing Gestalt and Meaningfully Creating Gestalt, Systematically Described and with Numerous Examples Explained, 1. Text-Volume, 2. Plate-Volume, in German], Münster: Böhlau, viii + 139 and vi + 192 pp.

2.2 Works on pattern creation and pattern analysis

2.2.1 Pattern creation

Binkley, T. (1992) Symmetry Studio: Computer-Aided Surface Design, [Software created by T. Binkley and J. F. Simon, Jr.], New York: Van Nostrand Reinhold, viii + 198 pp., 1 computer disk [Macintosh]

Field, M. and Golubitsky, M. (1992) Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature, Oxford: Oxford University Press, xii + 218 pp.

- German trans., Chaotische Symmetrien: Die Suche nach Mustern in Mathematik, Kunst und Natur, Basel: Birkhäuser, 1993, 218 pp.

- French trans., La Symétrie du chaos: A la recherche des liens entre mathématiques, art et nature, Paris: Inter éditions, 1993, xii + 218 pp.

Gansweid, J. (1987) Symmetrie und Gestaltung: Optische Bewegungseffekte entwickelt aus geometrischen Elementen, [Symmetry and Arrangement <Creating Gestalt>: Optical-Kinetical Effects Developed with Geometrical Elements, in German], München: Callwey, 134 pp.

Kainuma, H. and Kainuma, Y. (1981) Patchiwaaku to shinmetorii, [Patchwork and Symmetry, in Japanese], Kasugai: Shinuma Yoshirou, 76 pp.

Lauwerier, H. (1995) Symmetrie, kunst en computers, [Symmetry, Art and Computers, in Dutch], Haarlem: Aramith, 120 pp., 1 compact disk.

McDowell, R. B. (1994) Symmetry: A Design System for Quiltmakers, Lafayette, California: C and T Publishers, 144 pp.

Waller, M. D. (1961) Chladni Figures: A Study in Symmetry, London: Bell, xxii + 163 pp. [Note: Visualization of sound waves - the sand pattern technique of Chladni (1756-1827) produces symmetric patterns on plates vibrated, for example, by a violin bow at their edges].

Also see
* Herfort and Klotz (1997) ® Section 1.1.2.

2.2.2 Pattern analysis: comprehensive surveys

Jablan, S. V. (1984) Teorija simetrije i ornament, [in Serbo-Croatian], Beograd: APXAIA, 344 pp.

- English trans., revised, Theory of Symmetry and Ornament, Beograd: Matematicki institut, 1995, 331 pp.
* WWW-version, Symmetry and Ornament,, 1999.

Lauwerier, H. A. (1988) Symmetrie: Regelmatige structuren in de kunst, [Symmetry: Regular Structures in Art, in Dutch], Amsterdam: Aramith, 140 pp.

Lockwood, E. H. and Macmillan, R. H. (1978) Geometric Symmetry, Cambridge [England]: Cambridge University Press, x + 228 pp.

Müller, C. (1985) Symmetrie und Ornament: Eine Analyse mathematischer Strukturen der darstellenden Kunst, [Symmetry and Ornament: An Analysis of Mathematical Structures in Representational Art, in German], Opladen: Westdeutscher Verlag, 51 pp.

Shepard, A. O. (1948) The Symmetry of Abstract Design with Special Reference to Ceramic Decoration, Contributions to American Anthropology and History, Vol. 9, No.47, Washington, D.C.: Carnegie Institution of Washington, Publication No. 574, [Separate pamphlet in Vol. 9, paginated as 209-293].

Stevens, P. S. (1981) Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions, Cambridge, Massachusetts: MIT Press, 400 pp.
* Paperback ed., ibid., 1981; Many new printings.

Washburn, D. K. and Crowe, D. W. (1988) Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, Seattle, Wash.: University of Washington Press, x + 299 pp.
* Paperback ed., ibid., 1991.

Also see
* Bérczi (1990) ® Section 1.1,
* Huff (1967-77, Parts 2-3), Kumagai and Sawada (1983) ® Section 1.1.3,
* Crowe (1986), Roanes and Roanes (1993) ® Section and 1.1.2.
* Takahashi (1998) ® Section 1.2.1,
* Jaskowski (1952), Shubnikov (1940) ® Section 2.1.1,
* Shubnikov and Koptsik (1972), Wolf and Wolff (1956), and some other books ® Section 2.1.2.

2.2.3 Pattern analysis: special fields

Abas, S. J. and Salman, A. S. (1995) Symmetries of Islamic Geometrical Patterns, [With forewords by M. Atiyah and A. Moustafa], Singapore: World Scientific, xxii + 396 pp, 16 color plates.

Bérczi, S. (1986-87) Szimmetria és techné a magyar, avar és hanti díszítômüvészetben, [Symmetry and technê in the Hungarian, Avar, and Hanti Ornamental Art, in Hungarian], Budapest: Eötvös Loránd Tudományegyetem, Åltalános Technika Tanszék; Leuven, Belgium: Leuveni Katolikus Egyetem [Catholic University of Louvain], Collegium Hungaricum, 59 pp.

Gerdes, P. (1996) Lunda Geometry: Designs, Polyominoes, Patterns, Symmetries, Maputo, Mozambique: Universidade Pedagógica, 152 pp. [Lunda is a region of the North-Eastern part of Angola].

MacGillavry, C. H. (1965) Symmetry Aspects of M. C. Escher's Periodic Drawings, Utrecht: Oosthoek, [Published for the International Union of Crystallography], xi + 84 pp.
* 2nd ed., Utrecht: Bohn, Scheltema & Holkema, [Published for the International Union of Crystallography], 1976, xi + 84 pp.
* American reprint ed., Fantasy and Symmetry: The Periodic Drawings of M. C. Escher, New York: Abrams, 1976, xi + 84 pp.

- Japanese trans., Esshaa: Shinmetorii no sekai, [Escher: The World of Symmetry, in Japanese], [With an afterword by K. Fushimi (Husimi)], Tokyo: Saiensusha, 1981, 90 pp.

Otto, B. (1976) Geometrische Ornamente auf anatolischer Keramik: Symmetrien frühester Schmuckformen im nahen Osten und in der Ägäis, [Geometrical Ornaments on Anatolian Ceramics: Symmetries of the Earliest Decoration-Forms in the Near East and in the Aegean, in German], Mainz am Rhein: von Zabern, xiii + 203 pp.

Plehn, A. L. (1911) Farbensymmetrie und Farbenwechsel: Prinzipien deutscher und italienischer Farbverteilung, [Color-Symmetry and Color-Change: Principles of German and Italian Color-Distribution, in German], Strassburg: Heitz, 90 pp. [This color-symmetry is not identical

Schattschneider, D. (1990) Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M. C. Escher, New York: Freeman, xiv + 354 pp.
* Paperback ed., ibid, 1992

- Japanese trans., Esshaa - hen'you no geijutsu: Shinmetori no hakken, [Escher - The Art of Transformation: The Discovery of Symmetry, in Japanese], Tokyo: Nikkei Saiensusha, 1991, xiii + 370 pp.

- French trans., Visions de la symétrie: Les Cahiers, les dessins périodiques et les oeuvres corrélatives de M. C. Escher, Paris: Seuil, 1992, 368 pp.

- Italian trans., Visioni della simmetria: I disegni periodici di M. C. Escher, [Visions of Symmetry: The Periodic Drawings of M. C. Escher, in Italian], Bologna: Zanichelli, 1992, xiii + 354 pp.

Tarayan, Z. R. (1989) Simvoly simmetrii ornamenta v armianskom prikladnom iskusstve, [Symbols of Ornamental Symmetry in Armenian Applied Arts, in Russian], Erevan, Armenia: Izdatel'stvo Akademii Nauk Armyanskoi SSR, 198 pp., 26 plates.

Washburn, D. K. (1977) A Symmetry Analysis of Upper Gila Area Ceramic Design, Papers of the Peabody Museum of Archaeology and Ethnology, Vol. 68, Cambridge, Massachusetts: Harvard University Press, xiii + 193 pp. [The Gila River rises in Sierra Madre, New Mexico, U.S.A., and crosses to the Colorado River in Arizona].

Also see
* Rull Perez (1987) ® Section,
* Lucich (1987), Witherspoon and Peterson (1995) ® Section 3.4.1.

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