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  • Cited by 9
Publisher:
Cambridge University Press
Online publication date:
May 2013
Print publication year:
2013
Online ISBN:
9781139014632

Book description

Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.

Awards

Honourable Mention, 2013 PROSE Award for Mathematics

Reviews

'Cucker [has] produced a pot au feu, an eclectic catch-all. There is much that can be learned from [his] presentation of the marriage of mathematics and art. I consider Manifold Mirrors Arcimboldesque in that it is an assemblage of many basic mathematical ideas and constructs, [adding] up to … well, to a unique work.'

Philip J. Davis Source: SIAM News

'… there is certainly something new to be discovered for every reader. The book grew out of a course, and so it is obviously possible to extract some interesting lectures from the material that is presented.'

Source: The European Mathematical Society (euro-math-soc.eu)

'The merits of this big, ambitious book greatly exceed its deficiencies. Felipe Cucker’s immense learning, and his often densely technical presentation of mathematical complexities, are balanced by a pervasive lightness of tone and by a flair for offbeat allusions that range from Euripides to Busby Berkeley. His book is a joy for the eye and a feast for the mind.'

Hardy Grant Source: MAA Reviews

'Mathematical material is complete and rigorous, at an upper-division undergraduate level, with statements of relevant theorems and their proofs … Highly recommended. Upper-division undergraduates and faculty.'

C. A. Gorini Source: Choice

'This is an impressive and ambitious book and is one well-worth taking time to work through.'

Richard Talbot Source: Nexus Network Journal

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Contents

References
References
Abbott, E. (1987). Flatland: A Romance of Many Dimensions. London: Penguin.
Abish, W. (1974). Alphabetical Africa. New York: New Directions Books.
Alberti, L. B. (1991). On Painting. London: Penguin. Translated by C., Grayson with introduction and notes by M., Kemp.
Alder, K. (2002). The Measure of All Things. New York: The Free Press.
Alperson, P. (2004). Music: formalism and beyond. In P., Kivy, ed., The Blackwell Guide to Aesthetics. Oxford: Blackwell. pp. 254–75.
Andersen, K. (2007). The Geometry of an Art. New York: Springer-Verlag.
Anglin, W. S. (1997). The Philosophy of Mathematics: The Invisible Art. Lewiston, NY: Edwin Mellen Press.
Antonova, C. (2010). On the problem of “reverse perspective”: definitions East and West. Leonardo, 43(5), 464–9.
Arnheim, R. (1984). Art and Visual Perception: A Psychology of the Creative Eye. Berkeley, CA: University of California Press.
Asimov, I. (1983). The Universe: From Flat Earth to Black Holes and Beyond, 3rd edn. London: Penguin.
Balanchine, G. (1968). Balanchine's New Complete Stories af the Great Ballets. Garden City, NY: Doubleday. Edited by F., Mason with drawings by M., Becket.
Baloglou, G. (2007). Isometrica: A Geometrical Introduction to Planar Crystallographic Groups. Online version available at http://www.emis.de/monographs/Isometrica.
Banham, M. (1995). The Cambridge Guide to Theatre. Cambridge: Cambridge University Press.
Barber, E. J. W. (1991). Prehistoric Textiles: The Development of Cloth in the Neolithic and Bronze Ages. Princeton, NJ: Princeton University Press.
Bazin, A. (1960). The ontology of the photographic image. Film Quarterly, 13(4), 4–9.
Begley, W. (1992). Biblia Anagramatica. Whitefish, MT: Kessinger Publishing LLC. Reprint from the original 1904 edition published in London by Hazel, Watson, and Viney. Curiously, the original edition has two m's in Anagrammatica but the reprint spells the word in the cover with only one.
Belkin, K. L. (1998). Rubens. London: Phaidon.
Benson, D. (2007). Music: A Mathematical Offering. Cambridge: Cambridge University Press.
Bernstein, L. (1976). The Unanswered Question. Six Talks at Harvard. Cambridge, MA: Harvard University Press.
Birkhoff, G. D. (1933). Aesthetic Measure. Cambridge, MA: Harvard University Press.
Blake, W. (1970). Songs of Innocence and Experience. Oxford: Oxford University Press.
Blunt, A. (1979). Borromini. Cambridge, MA: Harvard University Press.
Booker, P. J. (1963). A History of Engineering Drawing. London: Chatto & Windus.
Borges, J. L. (1964). Other Inquisitions. Austin, TX: University of Texas Press.
Bostock, D. (2009). Philosophy of Mathematics. Chichester: Wiley-Blackwell.
Bourdon, D. (1989). Warhol. New York: Harry N. Abrams, Inc.
Brewster, D. (1819). Treatise on the Kaleidoscope. Edinburgh: Archibald Constable & Co.
Bühler, W. K. (1981). Gauss: A Biographical Study. New York: Springer Verlag.
Burke, E. (1990). A Philosophical Enquiry into the Origin of our Ideas of the Sublime and Beautiful. The World's Classics. Oxford: Oxford University Press.
Butler, S. (1967). Hudibras. Oxford: Oxford University Press.
Caillois, R. (2001). Man, Play and Games. Urbana, IL: University of Illinois Press.
Campbell, G. (2001). The life records. In T. H., Corns, ed., A Companion to Milton. Oxford: Blackwell. pp. 483–98.
Carey, J. ed. (2000). John Donne: The Major Works. Oxford: Oxford University Press.
Carroll, L. (1993). Alice's Adventures in Wonderland & Through the Looking-Glass. Ware: Wordsworth.
Carroll, N. (2003). Dance. In J., Levinson, ed., The Oxford Handbook of Aesthetics. Oxford: Oxford University Press. pp. 583–93.
Cederberg, J. N. (2001). A Course in Modern Geometries, 2nd edn. Undergraduate Texts in Mathematics. New York: Springer-Verlag.
Cheney, L. (1997). Stylistic problems in Mannerism and Maniera. In L., Cheney, ed., Readings in Italian Mannerism. New York: Peter Lang. pp. 1–8.
Cook, T. A. (1979). The Curves of Life. New York: Dover Publications, Inc.
Coxeter, H. S. M. (1979). The non-Euclidean symmetry of Escher's picture “Circle Limit III”. Leonardo, 12, 19–25.
Culler, J. (1997). Literary Theory: A Very Short Introduction. Oxford: Oxford University Press.
Da Vignola, J. B. (1987). Le Due Regole della Prospettiva Practica. Alburgh: Archival Facsimiles Limited. A reproduction of the copy in the British Library.
Da Vinci, L. (2002). A Treatise on Painting. New York: Prometheus Books.
Darwin, C. R. (1962). On the Various Contrivances by which British and Foreign Orchids are Fertilised by Insects. London: John Murray. Online version available at http://darwin-online.org.uk.
Davies, P. (2000). Antique Kilims of Anatolia. New York: W.W. Norton & Company.
Delacroix, E. (1938). The Journal of Eugène Delacroix. London: Jonathan Cape.
Descartes, R. (1954). The Geometry. New York: Dover Publications, Inc. Translated from the French and Latin by D. E., Smith and M. L., Latham. With a facsimile of the first edition.
Diderot, D. (2000). Art. In I., Frank, ed., The Theory of Decorative Art: An Anthology of European & American Writings, 1750–1940. New Haven: Yale University Press. pp. 139–49.
Dubery, F. and Willats, J. (1983). Perspective and Other Drawing Systems. New York: Van Nostrand Reinhold Co.
Dye, D. S. (1974). Chinese Lattice Designs. New York: Dover Publications, Inc.
Eckler, R. (1996). Making the Alphabet Dance. New York: St. Martin's Press.
Eco, U. (ed.) (2004). On Beauty: A History of a Western Idea. London: Secker & Warburg.
Edgerton, S. Y. (2009). The Mirror, the Window, and the Telescope. Ithaca, NY: Cornell University Press.
Einstein, A. (1926). Entry Space-Time in the 13th edition of the Encyclopedia Britannica.
Eliot, T. S. (1968). Four Quartets. London: The Folio Society.
Ellis, J. (1992). Visible Fictions. London: Routledge.
Elster, J. (1983). Sour Grapes. Cambridge: Cambridge University Press.
Euclid, , (1956). The Thirteen Books of The Elements, 2nd edn. New York: Dover. Translated with introduction and commentary by Sir Thomas L., Heath.
Euripides, , (2000). Hecuba; The Trojan Women; Andromache. Oxford: Oxford University Press. Translated with explanatory notes by J., Morwood.
Fahr-Becker, G. (1994). Japanese Prints. Köln: Taschen.
Farish, W. (1822). On isometrical perspective. Transactions of the Cambridge Philosophical Society.
Feldman, M. (1985). Crippled symmetry. In W., Zimmermann, ed., Morton Feldman Essays. Köln: Beginner Press. pp. 124–37.
Feynman, R., Leighton, R. B. and Sands, M. (19631965). The Feynman Lectures on Physics. Reading, MA: Addison-Wesley.
Field, J. V. (2005). Piero della Francesca: A Mathematician's Art. New Haven, NJ: Yale University Press.
Fink, R.Repeating Ourselves: American Minimal Music as Cultural Practice. Berkeley, CA: University of California Press.
Flannagan, R. (2002). John Milton. Oxford: Blackwell Publishing.
Flocon, A. and Barre, A. (1987). Curvilinear Perspective. Berkeley, CA: University of California Press.
Ford, P. R. J. (1989). Oriental Carpet Design. London: Thames and Hudson.
Fong, W. and Fu, M. (1973). Metropolitan Museum of Art (New York, NY). Sung and Yuan Paintings. New York: distributed by New York Graphic Society.
Forkel, J. N. (1920). Johann Sebastian Bach. His Life, Art, and Work. London: Constable and Co.
Fry, E. F. (1966). Cubism. London: Thames and Hudson.
Gao, J. (1996). The Expressive Act in Chinese Art. Uppsala: Academiae Ubsaliensis.
Gluck, C. W. (1962). Collected Correspondence and Papers. New York: St. Martin's Press. Edited by H. and E. H. Mueller, von Asow. Translated by S., Thomson.
Gödel, K. (1967). The completeness of the axioms of the functional calculus. In J., van Heijenoort, ed., A Source Book in Mathematical Logic. Cambridge, MA: Harvard University Press. pp. 582–91.
Gombrich, E. H. (1982). The Image and the Eye: Further Studies in the Psychology of Pictorial Representation. London: Phaidon.
Gombrich, E. H. (1984). The Sense of Order, 2nd edn. London: Phaidon.
Gombrich, E. H. (1989). The Story of Art, 15th edn. Englewood Cliffs, NJ: Prentice Hall.
Greenberg, M. J. (1993). Euclidean and Non-Euclidean Geometries, 3rd edn. New York: W.H. Freeman and Company.
Greene, G. (1990). In memory of Borges. In Reflections, London: Penguin Books. pp. 306–7.
Hanslick, E. (1986). On the Musically Beautiful: A Contribution towards the Revision of the Aesthetics of Music. Indianapolis, IN: Hackett. Translated by G., Payzant.
Harrison, C. and Wood, P. (eds). (1992). Art in Theory: 1900–2000, An Anthology of Changing Ideas. Oxford: Blackwell.
Hartshorne, R. (1997). Geometry: Euclid and Beyond, 2nd edn. Undergraduate Texts in Mathematics. New York: Springer-Verlag.
Hauser, A. (1962). The Social History of Art. London: Routledge. Four volumes edition.
Hilbert, D. (1987). Foundations of Geometry, 2nd edn. Chicago: Open Court.
Hironobu, K. (1991). Narrative illustration in the handscroll format. In A., Murck and W. C., Fong, eds, Words and Images: Chinese Poetry, Calligraphy, and Painting. New York: The Metropolitan Museum of Art. pp. 247–66.
Hodges, W. (2003). The geometry of music. In J., Fauvel, R., Flood and R., Wilson, eds, Music and Mathematics: From Pythagoras to Fractals. Oxford: Oxford University Press. pp. 91–111.
Hofstadter, D. (1979). Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books.
Hofstadter, D. (2002). Mystery, classicism, elegance: an endless chase after magic. In D., Schattschneider and M., Emmer, eds, M.C. Escher's Legacy: A Centennial Celebration. Berlin: Springer-Verlag, pp. 24–51.
Hogarth, W. (1753). The Analysis of Beauty, Written with a View of Fixing the Fluctuating Ideas of Taste. London.
Horemiss, S. (1970). Optical and Geometrical Patterns and Designs. New York: Dover Publications, Inc.
Huizinga, J. (1998). Homo Ludens: A Study of the Play-Element in Culture. London: Routledge.
Jablan, S. V. (2002). Symmetry, Ornament and Modularity. Singapore: World Scientific. An online version is available at http://www.emis.de/monographs/jablan.
Jastrow, J. (1900). Fact and Fable in Psychology. Boston: Houghton Mifflin.
Johnson, S. (1984). Samuel Johnson: The Major Works.Oxford: OxfordUniversity Press. Edited with an introduction and notes by D., Greene.
Jones, O. (2001). Grammar of Ornament. New York: Dorling Kindersley.
Kant, I. (1952). Critique of Judgement. Oxford: Oxford University Press. Translated by J. C., Meredith.
Kant, I. (1997). Critique of Pure Reason. Cambridge: Cambridge University Press. Translated and edited by P., Guyer and A. W., Wood.
Kierkegaard, S. (1964). Repetition. An Essay in Experimental Psychology. New York: Harper & Row.
Kivy, P. (1993). The Fine Art of Repetition: Essays in the Philosophy of Music, Cambridge: Cambridge University Press. pp. 327–59.
Kivy, P. (ed.) (2004). The Blackwell Guide to Aesthetics. Oxford: Blackwell Publishing.
Kivy, P. (2009). Antithetical Arts: On the Ancient Quarrel Between Literature and Music. Oxford: Oxford University Press.
Krautheimer, R. in collaboration with T., Krautheimer-Hess. (1970). Lorenzo Ghiberti. Princeton, NJ: Princeton University Press.
Kristeller, P. O. (1965). The modern system of the arts. In P. O., Kristeller, ed., Renaissance Thought II: Papers on Humanism and the Arts. New York: Harper & Row. pp. 163–227.
Langer, S. (ed.) (1953). Feeling and Form. New York: Scribners.
Lanham, R. A. (1991). A Handlist of Rhetorical Terms. Berkeley, CA: University of California Press.
Levinson, A. (1974). The spirit of the classic dance. In S. J., Cohen, ed., Dance as a TheatreArt. New York: Dodd, Mead & Co. pp. 113–17.
Lew, J. (1989). Making city planning a game. The New York Times, 15 June.
Lorand, R. (2000). Aesthetic Order: A Philosophy of Order, Beauty and Art. London: Routledge.
Lucie-Smith, E. (1995). Artoday. London: Phaidon.
Luminet, J.-P. (2008). The Wraparound Universe. Wellesley, MA: A K Peters, Ltd.
Mackenzie, C. (1955). My Record of Music. New York: Putnam.
Manetti, A. (1970). The Life of Brunelleschi. University Park, PA: The Pennsylvania State University Press. Introduction, notes and critical text edition by H., Saalman.
Manguel, A. (2006). With Borges. London: Telegram Books.
Martin, J. (ed.) (1972). The Modern Dance. Brooklyn, NY: Dance Horizons.
Mathews, H. and Brotchie, A. (ed.) (1998). Oulipo Compendium. London: Atlas Press.
McArthur, T. (1995). Rhythm, rhyme and reason: the power of patterned sound. In R., Beard, ed., Rhyme: Reading and Writing. London: Hodder & Stoughton. pp. 23–41.
McCausland, S. (ed.) (2003). Gu Kaizhi and the Admonitions Scrolls. London: The British Museum Press.
Mertens, W. (1983). American Minimal Music. London: Kahn & Averill.
Motte, W. F. Jr (ed.) (1998). Oulipo: A Primer of Potential Literature. Normal, IL: Dalkey Archive Press.
Mukarrovský, J. (1978). The aesthetic norm. In J., Mukarrovský, ed., Structure, Sign, and Function: Selected Essays. New Haven, CT: Yale University Press. pp. 49–54. Translated and edited by J., Burbank and P., Steiner.
Oliver, M. (1998). Rules for the Dance: A Handbook for Writing and Reading Metrical Verse. Boston, MA: Houghton Mifflin Co.
Ortega y Gasset, J. (1968). The Dehumanization of Art and Other Essays on Art, Culture, and Literature. Princeton, NJ: Princeton University Press.
Owen, R. (2008). Piero della Francesca masterpiece ‘holds clue to 15th-century murder”. The Sunday Times, 23 January.
Pamuk, O. (2001). My Name is Red. London: Faber and Faber. English translation by E., Göknar.
Panofsky, E. (1971). The Life andArt of Albrecht Dürer. Princeton, NJ: Princeton University Press.
Panofsky, E. (1991). Perspective as Symbolic Form. New York: Zone Books.
Pater, W. (1986). The Renaissance. Studies in Art and Poetry. The World's Classics. Oxford: Oxford University Press.
Penrose, L. S. and Penrose, R. (1958). Impossible objects: a special type of visual illusion. British Journal of Psychology, 49, 31–3.
Perec, G. (1969). La Disparition. Paris: Denoël.
Perec, G. (1972). Les Revenentes. Paris: Editions Julliard.
Perec, G. (1986). History of the lipogram. In W. F., Motte Jr, ed., Oulipo: A Primer of Potential Literature. Normal, IL: Dalkey Archives Press. pp. 97–108.
Perec, G. (1995). A Void. London: Harvill Press. A translation of La Disparition by G., Adair.
Perec, G. (1996). The Exeter text: jewels, secrets, sex. In Three by Perec. Jaffrey, NH: David R. Godine – Publisher. pp. 55–120. A translation of Les Revenentes by I., Monk.
Piaget, J. (1977). The Moral Judgement of the Child. London: Penguin.
Pirenne, M. H. (1970). Optics, Painting & Photography. Cambridge: Cambridge University Press.
Plato, . (1994). Republic. Oxford: Oxford University Press. Translated by R., Waterfield.
Pope, A. (1966). Selected Poetry. The World's Classics. Oxford: Oxford University Press.
Propp, V. (1968). Morphology of the Folktale. Austin, TX: University of Texas Press. Translated by L., Scott.
Prout, E. (1890). Counterpoint: Strict and Free. London: Augener.
Prout, E. (1903). Harmony: Its Theory and Practice. London: Augener.
Rahn, J. (2000). Music Inside Out: Going Too Far in Musical Essays. London: Routledge.
Read, H. (1961). Art and Industry. New York: Horizon Press.
Reichardt, J. (1974). Pop art. In T., Richardson and N., Stangos, eds, Concepts of Modern Art. Harmondsworth: Penguin Books. pp. 238–42.
Richards, I. A. (1995). Principles of Literary Criticism. London: Routledge.
Robbins Landon, H. C. (1961). A pox on Manfredini. High Fidelity, 11(6), 38–9, 86–7.
Robson, J. (ed.) (1997). Music and Meaning. Ithaca, NY: Cornell University Press.
Rodríguez, H. (2006). Metaesthesis. In K., Oosterhuis and L., Feireiss, eds, Game-SetAndMatch II. On Computer Games, Advanced Geometries and Digital Technologies. Rotterdam: Episode Publishers. pp. 574–81.
Rodríguez, H. (2008). Constraint, cruelty and conversation. In M., Hjort, ed., dekalog 1: On The Five Obstructions. London: Wallflower Press. pp. 38–56.
Rollins, A. and Adams, E. (2003). Andrew Rollins and Ernest Adams on Game Design. Indianapolis, IN: New Riders.
Sacks, O. (2008). Musicophilia. London: Picador.
Sarduy, S. (1974). Barroco. Buenos Aires: Sudamericana.
Schattschneider, D. (1990). Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M.C. Escher. New York: W.H. Freeman.
Seckel, A. (2004). Masters of Deception. New York: Sterling Publishing Co.
Shakespeare, W. (1951). The Complete Works. London: Collins. With an introduction and glossary by P., Alexander.
Silbergeld, J. (1982). Chinese Painting Style: Media, Methods, and Principles of Form. Seattle, WA: University of Washington Press.
Soames, S. (2003). Philosophical Analysis in the Twentieth Century, volume 1. Princeton, NJ: Princeton University Press.
Sontag, S. (1967). Against Interpretation and Other Essays. London: Eyre & Spottiswoode.
Stravinsky, I. (1960). Poetics of Music. New York: Random House.
Strunk, O. (ed.) (1980). Source Readings in Music History. New York: W.W. Norton.
Summers, D. (2003). Real Spaces: World Art History and the Rise of Western Modernism. London: Phaidon.
Summers, J. (1994). Oriental Rugs. New York: Crown Publishers, Inc.
Tarski, A. (1959). What is elementary geometry? In L., Henkin, P., Suppes and A., Tarski, eds, The Axiomatic Method. Amsterdam: North-Holland. pp. 16–29.
Tent, M. B. W. (2006). The Prince of Mathematics: Carl Friedrich Gauss. Wellesley, MA: A K Peters, Ltd.
Thompson, D. W. (1961). On Growth and Form. Cambridge: Cambridge University Press. Abridged and edited by J. T., Bonner.
Todd, S. and Latham, W. (1992). Evolutionary Art and Computers. London: Academic Press.
Van Briessen, F. (1998). The Way of the Brush. Painting Techniques of China and Japan. Boston, MA: Tuttle Publishing.
Van Gogh, V. (2009). The Letters, volume 4. London: Thames and Hudson. Edited by L., Jansen, H., Luitjen and N., Bakker.
Van Sijll, J. (2005). Cinematic Storytelling: The 100 Most Powerful Film Conventions Every Filmmaker Must Know. Studio City, CA: Michael Wiese Productions.
Vasari, G. (1991). The Lives of the Artists. Oxford: Oxford University Press.
Vitruvius, M. (1999). De Architectura. Cambridge: Cambridge University Press. Translated from Latin by I. D., Rowland.
Weeks, J. R. (1985). The Shape of Space. New York: Marcel Dekker.
Weyl, H. (1952). Symmetry. Princeton, NJ: Princeton University Press.
Willats, J. (1997). Art and Representation. Princeton, NJ: Princeton University Press.
Wu, H. (1996). The Double Screen: Medium and Representation in Chinese Painting. London: Reaktion Books.
Wulff, O. (1907). Die ungekehrte Perspektive und die Niedersicht. Eine Raumanschauungsform der albyzantischen Kunst und ihre Fortbildung in der Renaissance. In H., Weizsäcker, ed., Kunstwissenschaftliche Beiträge August Schmarsow gewidmet zum fünfzigsten Semester seiner akademischen Lehrtätigkeit. Leipzig: K.W. Hiersemann. pp. 3–42.
Wynn, T. (2002). Archaeology and cognitive evolution. Behavioral and Brain Sciences, 25, 389–402.
Yeats, W. B. (2001). Yeats's Poems. Basingstoke: Palgrave. Edited and annotated by A.N., Jeffares.

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