Abstract
The hall of the 1986 Venice Biennale dedicated to Art and Science opened with works by Lucio Saffaro (the artist whose works are featured on all the covers of books in the Imagine Math book series), along with Felice Ragazzo’s reconstruction of Kepler’s model of how the universe works, when Kepler still believed that the orbits of the planets were circular and circumscribed by the regular solids first described by Plato [27, 5, 28, 6, 8, 9].
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Notes
- 1.
Eng. trans, Johannes Kepler, The Harmony of the World, E. J. Aiton, A. M. Duncan and J. V. Field, Philadelphia, American Philosophical Society, 1997, p. 397-398.
- 2.
Eng. trans, Johannes Kepler, The Harmony of the World, E. J. Aiton, A. M. Duncan and J. V. Field, Philadelphia, American Philosophical Society, 1997, p. 116.
- 3.
The well-known Steiner’s Surface (or Roman Surface, so-called because according to the account given by Eugenio Beltrami (1835-1900) it was conceived by Jacob Steiner (1796-1863) during his stay in Rome in 1844) is a rational surface of degree 4 and class 3, of tetrahedral symmetry, of the Cartesian equation x 2 y 2 + y 2 z 2 + z 2 x 2 + xyz = 0.
References
Bibliotheca Perspectivae. I trattati di prospettiva del Rinascimento. http://brunelleschi.imss.fi.it/bdtema/ibpr.asp?c=684&xsl=5
J.-P. Bourguignon, M. Cassé, H. Chandès (eds.), Mathèmatiques, un dépaysement soudain, exhibition catalogue (Fondation Cartier pour l’art contemporain, Paris, 2012)
J.-P. Bourguignon, Mathematics, a beautiful elsewhere, in Imagine Math 3, ed. by M. Emmer (Springer, Heidelberg, 2014)
C. Boyer, History of mathematics (Wiley, New York, 1968)
M. Emmer, Lo spazio tra matematica e arte, in XLII Esposizione Internazionale d’Arte la Biennale di Venezia. Arte e scienza. Spazio. Colore ed. by G. Macchi, et al. (Edizioni La Biennale, Venice, 1986), pp. 36–39
M. Emmer, Computers, film DVD, series Art and Mathematics, 25 m., colour. Film 7 prod. (M. Emmer, Rome, partially filmed at the Biennale of Venice, 1986)
M. Emmer, Platonic Solids, film DVD, series Art and Mathematics, 25 m., colour. Film 7 prod (M. Emmer, Roma, 1986)
M. Emmer, (ed.), L’occhio di Horus: itinerari nell’immaginario matematico, exhibition catalogue (Istituto dell’Enciclopedia Italiana, Rome, 1989)
M. Emmer, (director and ed.), L’occhio di Horus, film, 30 m. RAI prod. (1989)
M. Emmer (ed.), The visual mind: art and mathematics (MIT Press, Cambridge, MA, 1993)
M. Emmer (ed.), The visual mind II: art and mathematics (MIT Press, Cambridge, MA, 2005)
M. Emmer, Visibili armonie: arte cinema teatro e matematica (Bollati Boringhieri, Torino, 2007)
M. Emmer, Il Mazzocchio da Paolo Uccello a Lucio Saffaro, in Matematica e cultura 2008, ed. by M. Emmer (Springer, Milan, 2008), pp. 111–126
M. Emmer, Bolle di sapone tra arte e matematica (Bollati Boringhieri, Torino, 2009)
M. Emmer, Sinisgalli tra arte, cinema e tecnologia, in Un Leonardo del Novecento: Leonardo Sinisgalli, PRISTEM, Note di matematica, storia, cultura, 23-24 edn, ed. by G.I. Bischi, P. Nastati, (2009) pp. 148–178
M. Emmer, I numeri immaginari: cinema e matematica (Bollati Boringhieri, Torino, 2011)
M. Emmer, Sinisgalli tra cinema, poesia e matematica, in Il guscio della chiocciola. Studi su Leonardo Sinisgalli, ed. by S. Martelli, F. Vitelli, vol. I (Edisud, Forum Italicum, Stony Brook, NY, Salerno, 2012), pp. 31–43
M. Fabre de Lagrange, A catalogue of a collection of models of ruled surfaces; With an appendix, containing an account of the application of analysis to their investigation and classification by C.W. Merrifield, (George E. Eyre and William Spottiswoode, London 1872). http://catalog.hathitrust.org/Record/006085625
I. Fortunè, Man Ray et les objets mathématiques. Études photographiques 6, May 1999 (1999). http://etudesphotographiques.revues.org/190
E. Gamba, The Mathematical Ideas of Luca Pacioli Depicted by Iacopo de’ Barbari in the ‘doppio ritratto’, in Imagine Math, ed. by M. Emmer (Springer, Milan, 2012), pp. 267–271
S. Günther, Vermischte Untersuchungen zür Geschichte der Mathematischen Wissenschaften, Leipzig, (1876)
L.D. Henderson, The fourth dimension and non-Euclidean geometry in modern Art (Princeton University Press, Princeton, 1983)
L.D. Henderson, Duchamp in context (Princeton University Press, Princeton, 1998)
L.D. Henderson, The fourth dimension and non-euclidean geometry in modern art rev (MIT Press, Cambridge, MA, 2013)
G. N. Lautréamont, (I. L. Ducasse), Les Chants de Maldoror, in Lautréamont, Germain Nouveau, OEuvres complètes, ed. by P.-O. Walzer (Gallimard, Paris, 1970) (Eng. trans. R. J. Dent trans. The songs of Maldoror, (Chicago, University of Chicago Press, 2011))
G. Macchi et al. (eds.), XLII Esposizione Internazionale d’Arte la Biennale di Venezia. Arte e scienza. Spazio. Colore (Edizioni La Biennale, Venice, 1986)
G. Macchi, Verso l’undicesima dimensione. In XLII Esposizione Internazionale d’Arte la Biennale di Venezia. Arte e scienza. Spazio. Colore. Section catalogue, ed. by G. Macchi, et al. (Edizioni La Biennale, Venice, 1986), pp. 45–46
G. Macchi, Spazio, in XLII Esposizione Internazionale d’Arte la Biennale di Venezia, General Catalogue ed. by M.-G. Gervasoni (Edizioni La Biennale, Venice, 1986), pp. 51–65
P. Montel (ed.), Formes: Mathèmatiques, peintres, sculpteurs contemporaines (Universitè de Paris, Palais de la Découverte, Paris, 1963)
N. Palladino, F. Palladino, I modelli matematici costruiti per l’insegnamento delle matematiche superiori pure ed applicate. Ratio Mathematica 19, 31–88 (2009)
B. Phipps, (ed.), Intersections: Henry Moore and stringed surfaces, exhibition catalogue (Royal Society, London, 2012). http://royalsociety.org/uploadedFiles/Royal_Society_Content/z_events/2012/Intersections%202012-04-04.pdf
Plato: Timaeus. Eng. trans. Benjamin Jowett, in Plato. The Collected Dialogues including the Letters, ed. by E. Hamilton, C. Huntington (Princeton University Press, Princeton, 1961)
H. Poincaré, La Science et l’Hypothèse (Flammarion, Paris, 1902) (Eng. trans. W. J. Greenstreet, trans. Science and Hypothesis (Walter Scott Publishing, New York, 1905)
L. Saffaro, Dai cinque poliedri all’infinito (Annuario EST Mondadori, 1976), pp. 473–484
L. Saffaro, Anticipazioni e mutamenti nel pensiero geometrico, in L’occhio di Horus: itinerari nell’immaginario matematico, ed. by M. Emmer (Istituto della Enciclopedia Italiana, Roma, 1989), pp. 105–116
L. Sinisgalli (concept), V. Sabel (direction), Una lezione di geometria. Film, 12 min., b&w. Screenplay L. Sinisgalli, photo. M. Bava, music G. Petrassi, prod. C. Ponti (1948)
L. Sinisgalli, Carciopholus Romanus, in Furor Mathematicus, ed. by L. Sinisgalli (Mondadori, Milan, 1950), pp. 29–30
L. Sinisgalli, Geometria barocca. Pirelli 3, 44–45 (1950)
L. Sinisgalli, Macchine celibi. Il Mattino di Napoli, 28 agosto 1978. Rpt in: Sinisgalli e i ragazzi di via Panisperna, ed. by L. Bonolis, D. Cocolicchio, B. Russo, in Un Leonardo del Novecento: Leonardo Sinisgalli. PRISTEM, Note di matematica, storia, cultura ed. by G. I. Bischi, P. Nastati, (2009), pp. 23–24, 13–14
H. Sugimoto, Official home page. http://www.sugimotohiroshi.com/ (2013)
J. Toland, Intersections: Henry Moore and stringed surfaces: In: Intersections: Henry Moore and stringed surfaces, exhibition catalogue, ed. by Phipps, B. (Royal Society, London, 2012), pp. 3–4
J. Wess, The History of Mathematical Surface Models, in Intersections: Henry Moore and stringed surfaces, exhibition catalogue, ed. by Phipps, B. (Royal Society, London, 2012), pp. 7–8
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Emmer, M. (2015). Visible Harmonies: Mathematical Models. In: Emmer, M. (eds) Imagine Math 3. Springer, Cham. https://doi.org/10.1007/978-3-319-01231-5_6
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