The Divine Proportion
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Symmetry As an Aesthetic Factor
Comp. & Maths. with Appls, Vol. 12B, Nos. I/2, pp. 77-82. 1986 0886-9561/86 $3,1)0+ .00 Printed in Great Britain. © 1986 Pergamon Press Ltd. SYMMETRY AS AN AESTHETIC FACTOR HAROLD OSBORNEt Kreutzstrasse 12, 8640 Rappersvill SG, Switzerland Abstract--In classical antiquity symmetry meant commensurability and was believed to constitute a canon of beauty in nature as in art. This intellectualist conception of beauty persisted through the Middle Ages with the addition doctrine that the phenomenal world manifests an imperfect replica of the ideal symmetry of divine Creation. The concept of the Golden Section came to the fore at the Renaissance and has continued as a minority interest both for organic nature and for fine art. The modern idea of symmetry is based more loosely upon the balance of shapes or magnitudes and corresponds to a change from an intellectual to a perceptual attitude towards aesthetic experience. None of these theories of symmetry has turned out to be a principle by following which aesthetically satisfying works of art can be mechanically constructed. In contemporary theory the vaguer notion of organic unity has usurped the prominence formerly enjoyed by that of balanced symmetry. From classical antiquity the idea of symmetry in close conjunction with that of proportion dominated the studio practice of artists and the thinking of theorists. Symmetry was asserted to be the key to perfection in nature as in art. But the traditional concept was radically different from what we understand by symmetry today--so different that "symmetry" can no longer be regarded as a correct translation of the Greek word symmetria from which it derives--and some acquaintance with the historical background of these ideas is essential in order to escape from the imbroglio of confusion which has resulted from the widespread conflation of the two. -
De Divino Errore ‘De Divina Proportione’ Was Written by Luca Pacioli and Illustrated by Leonardo Da Vinci
De Divino Errore ‘De Divina Proportione’ was written by Luca Pacioli and illustrated by Leonardo da Vinci. It was one of the most widely read mathematical books. Unfortunately, a strongly emphasized statement in the book claims six summits of pyramids of the stellated icosidodecahedron lay in one plane. This is not so, and yet even extensively annotated editions of this book never noticed this error. Dutchmen Jos Janssens and Rinus Roelofs did so, 500 years later. Fig. 1: About this illustration of Leonardo da Vinci for the Milanese version of the ‘De Divina Proportione’, Pacioli erroneously wrote that the red and green dots lay in a plane. The book ‘De Divina Proportione’, or ‘On the Divine Ratio’, was written by the Franciscan Fra Luca Bartolomeo de Pacioli (1445-1517). His name is sometimes written Paciolo or Paccioli because Italian was not a uniform language in his days, when, moreover, Italy was not a country yet. Labeling Pacioli as a Tuscan, because of his birthplace of Borgo San Sepolcro, may be more correct, but he also studied in Venice and Rome, and spent much of his life in Perugia and Milan. In service of Duke and patron Ludovico Sforza, he would write his masterpiece, in 1497 (although it is more correct to say the work was written between 1496 and 1498, because it contains several parts). It was not his first opus, because in 1494 his ‘Summa de arithmetic, geometrica, proportioni et proportionalita’ had appeared; the ‘Summa’ and ‘Divina’ were not his only books, but surely the most famous ones. For hundreds of years the books were among the most widely read mathematical bestsellers, their fame being only surpassed by the ‘Elements’ of Euclid. -
Impronte D'arte
Impronte d’Arte [Traces of Art] Comune di Forlì ImproImpronten d’Arte d’TracesArt of Art e Ufficio Informazione e Accoglienza Turistica Piazzetta della Misura, 5 - 47121 Forlì Tel. +39.0543.712.435 Fax +39.0543.712.755 e-mail: [email protected] www.turismoforlivese.it URP - Informagiovani Piazzetta della Misura, 5 - 47121 Forlì Tel. +39.0543.712.444/5 Fax +39.0543.712.450 e-mail: [email protected] [email protected] www.comune.forli.fc.it www.informagiovani.comune.forli.fc.it Impronte d’arte Fonti bibliografiche Traces of art Bibliographic sources Pubblicazione a cura dell’Unità Servizi Informativi (IAT-URP-Informagiovani) - Comune di Forlì AA.VV., Cara, vecchia città. Published by Unità Servizi Informativi (IAT-URP-Informagiovani) - Comune di Forlì Percorsi attraverso vie, chiese e palazzi di Forlì, Comune di Forlì, Forlì 1989 AA.VV., Benvenuti a Forlì, Comune di Forlì, Forlì 1990 AA.VV., La Provincia di Forlì-Cesena, Guide d’Italia, Touring Club italiano, Milano 2003 Archivio fotografico/photographs: Archivio Fotografico Unità Servizi Informativi e Ufficio E. Caruso, Forlì, Città e cittadini tra Ottocento e Novecento, I° vol., Edizione Girasole, Forlì 1990 Informazione e Accoglienza Turistica del Comune di Forlì, Archivio Fotografico Ufficio Stampa A. Colombi Ferretti, L. Prati (a cura di), Francesco Menzocchi, Forlì 1502-1574, Comune di Forlì Comune di Forlì, Archivio Fotografico Istituti Culturali del Comune di Forlì, Foto Giorgio Liverani, e Edisai srl, Ferrara 2003 Archivio Fotografico Provincia di Forlì-Cesena. A. Fabbri, Percorsi nella città, Provincia di Forlì-Cesena, Assessorato al Turismo, Forlì, ristampa giugno 2003 In copertina/cover images: Palazzo Orsi Mangelli, Particolare Rocca di Ravaldino, Monumento M. -
Simple Rules for Incorporating Design Art Into Penrose and Fractal Tiles
Bridges 2012: Mathematics, Music, Art, Architecture, Culture Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles San Le SLFFEA.com [email protected] Abstract Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1 1 Introduction M.C. Escher was the most prominent artist working with tessellations and space filling. Forty years after his death, his creations are still foremost in people’s minds in the field of tiling art. One of the reasons Escher continues to hold such a monopoly in this specialty are the unique challenges that come with creating Escher type designs inside a tessellation[15]. When an image is drawn into a tile and extends to the tile’s edge, it introduces incongruencies which are resolved by continuously aligning and refining the image. This is particularly true when the image consists of the lizards, fish, angels, etc. which populated Escher’s tilings because they do not have the 4-fold rotational symmetry that would make it possible to arbitrarily rotate the image ± 90, 180 degrees and have all the pieces fit[9]. -
Syddansk Universitet Review of "Henning, Herbert: La Divina
Syddansk Universitet Review of "Henning, Herbert: La divina proportione und die Faszination des Schönen oder das Schöne in der Mathematik" Robering, Klaus Published in: Mathematical Reviews Publication date: 2014 Document version Accepted author manuscript Citation for pulished version (APA): Robering, K. (2014). Review of "Henning, Herbert: La divina proportione und die Faszination des Schönen oder das Schöne in der Mathematik". Mathematical Reviews. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 14. Feb. 2017 MR3059375 Henning, Herbert La divina proportione und die Faszination des Sch¨onenoder das Sch¨onein der Mathematik. (German) [The divine proportion and the fascination of beauty or beauty in mathematics] Mitt. Math. Ges. Hamburg 32 (2012), 49{62 00A66 (11B39 51M04) The author points out that there is a special relationship between mathematics and the arts in that both aim at the discovery and presentation of truth and beauty. -
Leonardo Universal
Leonardo Universal DE DIVINA PROPORTIONE Pacioli, legendary mathematician, introduced the linear perspective and the mixture of colors, representing the human body and its proportions and extrapolating this knowledge to architecture. Luca Pacioli demonstrating one of Euclid’s theorems (Jacobo de’Barbari, 1495) D e Divina Proportione is a holy expression commonly outstanding work and icon of the Italian Renaissance. used in the past to refer to what we nowadays call Leonardo, who was deeply interested in nature and art the golden section, which is the mathematic module mathematics, worked with Pacioli, the author of the through which any amount can be divided in two text, and was a determined spreader of perspectives uneven parts, so that the ratio between the smallest and proportions, including Phi in many of his works, part and the largest one is the same as that between such as The Last Supper, created at the same time as the largest and the full amount. It is divine for its the illustrations of the present manuscript, the Mona being unique, and triune, as it links three elements. Lisa, whose face hides a perfect golden rectangle and The fusion of art and science, and the completion of the Uomo Vitruviano, a deep study on the human 60 full-page illustrations by the preeminent genius figure where da Vinci proves that all the main body of the time, Leonardo da Vinci, make it the most parts were related to the golden ratio. Luca Pacioli credits that Leonardo da Vinci made the illustrations of the geometric bodies with quill, ink and watercolor. -
Kepler's Cosmos
science and image Kepler’s cosmos Copernicus’s system of the Universe was revolutionary but his method of representing it on paper was anything but. It was left to Kepler to apply Renaissance techniques of spatial visualization to make the theory come alive. Martin Kemp icolaus Copernicus’s programme to 8 purge the Ptolemaic model of the Uni- Nverse of its growing burden of disfig- uring complications was driven not least by what we would call aesthetic considerations. The architecture of his heliocentric system reinstated the geometrical integrity that the Greek astronomers had sought: “At rest... in the middle of everything is the sun. For in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time?” Although Copernicus’s “temple” obeyed the principles of harmonically unified design advocated in the Renaissance, his conventionally diagrammatic representa- tion of his scheme in 1543 as a flat series of concentric circles did not avail itself of the new spatial vision inherent in the buildings and paintings of the Renaissance masters. It was more than 50 years later that Johannes Kepler, fervent Copernican and Platonist, allied the new visual forms with the new astronomical vision. Among the many testimonies to Kepler’s extraordinary powers of spatial visualiza- tion, none is more remarkable than the great cosmological model he illustrated in a fold- out plate in his Mysterium Cosmographicum of 1596. We know how the scheme came to be envisaged. He tells how, when he was teach- ing his “students the way Great Conjunc- tions jump eight signs at a time”, he drew Kepler’s “Model of the Orbits of the Planets” “many triangles, or quasi triangles, in the from Mysterium Cosmographicum, 1596 (above). -
Historical Painting Techniques, Materials, and Studio Practice
Historical Painting Techniques, Materials, and Studio Practice PUBLICATIONS COORDINATION: Dinah Berland EDITING & PRODUCTION COORDINATION: Corinne Lightweaver EDITORIAL CONSULTATION: Jo Hill COVER DESIGN: Jackie Gallagher-Lange PRODUCTION & PRINTING: Allen Press, Inc., Lawrence, Kansas SYMPOSIUM ORGANIZERS: Erma Hermens, Art History Institute of the University of Leiden Marja Peek, Central Research Laboratory for Objects of Art and Science, Amsterdam © 1995 by The J. Paul Getty Trust All rights reserved Printed in the United States of America ISBN 0-89236-322-3 The Getty Conservation Institute is committed to the preservation of cultural heritage worldwide. The Institute seeks to advance scientiRc knowledge and professional practice and to raise public awareness of conservation. Through research, training, documentation, exchange of information, and ReId projects, the Institute addresses issues related to the conservation of museum objects and archival collections, archaeological monuments and sites, and historic bUildings and cities. The Institute is an operating program of the J. Paul Getty Trust. COVER ILLUSTRATION Gherardo Cibo, "Colchico," folio 17r of Herbarium, ca. 1570. Courtesy of the British Library. FRONTISPIECE Detail from Jan Baptiste Collaert, Color Olivi, 1566-1628. After Johannes Stradanus. Courtesy of the Rijksmuseum-Stichting, Amsterdam. Library of Congress Cataloguing-in-Publication Data Historical painting techniques, materials, and studio practice : preprints of a symposium [held at] University of Leiden, the Netherlands, 26-29 June 1995/ edited by Arie Wallert, Erma Hermens, and Marja Peek. p. cm. Includes bibliographical references. ISBN 0-89236-322-3 (pbk.) 1. Painting-Techniques-Congresses. 2. Artists' materials- -Congresses. 3. Polychromy-Congresses. I. Wallert, Arie, 1950- II. Hermens, Erma, 1958- . III. Peek, Marja, 1961- ND1500.H57 1995 751' .09-dc20 95-9805 CIP Second printing 1996 iv Contents vii Foreword viii Preface 1 Leslie A. -
Leonardo Da Vinci's Study of Light and Optics: a Synthesis of Fields in The
Bitler Leonardo da Vinci’s Study of Light and Optics Leonardo da Vinci’s Study of Light and Optics: A Synthesis of Fields in The Last Supper Nicole Bitler Stanford University Leonardo da Vinci’s Milanese observations of optics and astronomy complicated his understanding of light. Though these complications forced him to reject “tidy” interpretations of light and optics, they ultimately allowed him to excel in the portrayal of reflection, shadow, and luminescence (Kemp, 2006). Leonardo da Vinci’s The Last Supper demonstrates this careful study of light and the relation of light to perspective. In the work, da Vinci delved into the complications of optics and reflections, and its renown guided the artistic study of light by subsequent masters. From da Vinci’s personal manuscripts, accounts from his contemporaries, and present-day art historians, the iterative relationship between Leonardo da Vinci’s study of light and study of optics becomes apparent, as well as how his study of the two fields manifested in his paintings. Upon commencement of courtly service in Milan, da Vinci immersed himself in a range of scholarly pursuits. Da Vinci’s artistic and mathematical interest in perspective led him to the study of optics. Initially, da Vinci “accepted the ancient (and specifically Platonic) idea that the eye functioned by emitting a special type of visual ray” (Kemp, 2006, p. 114). In his early musings on the topic, da Vinci reiterated this notion, stating in his notebooks that, “the eye transmits through the atmosphere its own image to all the objects that are in front of it and receives them into itself” (Suh, 2005, p. -
The Deep Space Mission That Might Trigger a Multidisciplinary Scientific Revolution by Judy Hodgkiss
II. Scientific Revolutions Will Shape the Future The Deep Space Mission that Might Trigger a Multidisciplinary Scientific Revolution by Judy Hodgkiss President Trump insists he wants the U.S. to lead Is There a Fundamental Principle of the world in scientific and technological develop- Development in the Universe? ment. He instinctively understands that the key to In 1921, Albert Einstein went beyond his relativity doing that is resuscitating and upgrading the U.S. theory, and put forward a theory of the cosmos, what he space program. called the concept of a “finite but unbounded” universe. As an example of the fundamentals of physical In a lecture that year before the Prussian Academy of economy, Lyndon LaRouche frequently pointed out Sciences, he asked the audience to consider a new met- how John F. Kennedy’s Apollo Project space mission aphor: He described the physical universe as a finite had provided the impetus for explosive growth of the number of shadows projected from different kinds of “Silicon Valley,” the previously higher-order geometries. He chal- bucolic rural area near San Jose, lenged the audience to not only California, which became Ameri- imagine the unseen geometries, ca’s high-tech center in the 1960s. but to imagine novel yardsticks LaRouche always insisted that that could measure them. Such a space exploration must be the universe would be bound only by point-on-the-spear in terms of the principles of development that scientific R&D. If the nation’s characterized it.1 frontier missions in space are ap- Einstein would be delighted propriately defined and fully- today to see examples of scien- funded, they not only provide tists in such fields as physics, spin-off benefits in innovative chemistry, or electronics, discov- ALMA technologies in obviously related Proto-planetary disc surrounding the young ering, to their amazement, that fields, but, even more impor- stellar object, Elias 2-27, 450 light-years away. -
FOR IMMEDIATE RELEASE August 18, 2015
FOR IMMEDIATE RELEASE August 18, 2015 MEDIA CONTACT Emily Kowalski | (919) 664-6795 | [email protected] North Carolina Museum of Art Presents M. C. Escher, Leonardo da Vinci Exhibitions and Related Events Raleigh, N.C.—The North Carolina Museum of Art (NCMA) presents two exhibitions opening in October 2015: The Worlds of M. C. Escher: Nature, Science, and Imagination and Leonardo da Vinci’s Codex Leicester and the Creative Mind. The Worlds of M. C. Escher features over 130 works (some never before exhibited) and will be the most comprehensive Escher exhibition ever presented in the United States. The Codex Leicester is a 500-year-old notebook handwritten and illustrated by inventor, scientist, and artist Leonardo da Vinci—the only manuscript by Leonardo in North America—that offers a glimpse into one of the greatest minds in history. “This is going to be an exciting fall at the Museum—an incredibly rare opportunity for our visitors to see not only centuries-old writings and sketches by Leonardo da Vinci, but also the work of M. C. Escher, another observer of nature and a perfect modern counterpart to Leonardo,” says NCMA Director Lawrence J. Wheeler. “These exhibitions will thrill art lovers and science lovers alike, and we hope that all visitors leave with a piqued curiosity, an ignited imagination, and a desire to more closely observe the world around them.” The Worlds of M. C. Escher: Nature, Science, and Imagination October 17, 2015−January 17, 2016 Comprising over 130 woodcuts, lithographs, wood engravings, and mezzotints, as well as numerous drawings, watercolors, wood blocks, and lithographic stones never before exhibited, The Worlds of M. -
Giovannino Battista: the Boy Baptist in Quattrocento Italian
COPYRIGHT AND USE OF THIS THESIS This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copyright Act permits an authorized officer of a university library or archives to provide a copy (by communication or otherwise) of an unpublished thesis kept in the library or archives, to a person who satisfies the authorized officer that he or she requires the reproduction for the purposes of research or study. The Copyright Act grants the creator of a work a number of moral rights, specifically the right of attribution, the right against false attribution and the right of integrity. You may infringe the author’s moral rights if you: - fail to acknowledge the author of this thesis if you quote sections from the work - attribute this thesis to another author - subject this thesis to derogatory treatment which may prejudice the author’s reputation For further information contact the University’s Director of Copyright Services sydney.edu.au/copyright San Giovannino: The Boy Baptist in Quattrocento Italian Art Georgina Sybella Macneil, 28 August 2013 Thesis submitted in fulfilment of requirements for the degree of Doctor of Philosophy (Ph.D.) Department of Art History and Film Studies, University of Sydney, Australia Abstract This thesis explores the imagery of the young John the Baptist in Renaissance art. The phenomenon of John’s juvenescence has been noted but insufficiently explored by previous scholarship.