Ma3032: Geometry for Art and Architecture

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MA3032: GEOMETRY FOR ART AND ARCHITECTURE Pre-requisite: Nil L T P C 3 1 0 3 Total Hours: 56 Hrs Module 1: Golden Ratio, polygons, tilings, the platonic solids and sacred geometry (14 hours) Great pyramid of Cheops, golden ratio, secrets of the great pyramid, squaring the circle, the rhind mathematical papyrus,rope stretchers triangle, music of the spheres, number symbolism, the equilateral triangle, tilings, hexagon & hexagram, pentagram & pentagon, golden triangle, the Timaeus, Polyhedra, polyhedra in art & architecture, vitruvius, ad quadratum, the sacred cut, pompeii and herculaneum, roman rectangle. Module 2: Number, Weight and Measure (14 hours) Biblical, classical and Islamic influences, symbolism of numbers and geometric figures, four & the square: the cross, tree of life, herms, pillars, five & the pentagon, six & the hexagon, seven & the heptagon, eight & the octagon, symbolism of the circle, celestial, ring, wheel, rainbow, crescent, calendar circles, stonehenge, the circle and gothic architecture. the gothic style, the masons, the gothic master plan, neolithic stone circles, mandala, hindu temple layout, Yin yang symbol. Module 3: Celestial themes in art and perspective (14 hours) The ptloemaic universe, the Sphaera mundi, the structuring of celestial space, nine ranks of angels, Dante's nine circles of heaven, Cigoli's Immacolata, portrayals of astronomers and allegories to astronomy, models of the cosmos, maps, globes, armillary spheres, orreries, domes, astonomical instruments, sundials, sun calendars, stone circles, twentieth-century astronomical art, sun symbols, temple orientation, pyramid placement, zodiac, radian measure, arc length, rotation, latitude and longitude, the conic sections, elliptical orbits ,perspective, Brunelleschi, Donatello, Masaccio, Mantegna, Alberti, from Euclid to Desargues, significance of perspective, later developments in perspective, perspective machines and cameras, The quadro or rectangular format,t he square format, the Tondo or round format, the roundel, Ovato Tondo and the elliptical format. Module 4: Dynamic symmetry, Art and the Computer, Chaos and Fractals (14 hours) Impact of the new geometries, the fourth dimension and physics on art, Lobachevski, Bolyai, Reimann, Einstein, Picasso, Braque, Mondrian, Malevich, abstraction, post-impressionism, cubism, constructivism , suprematism, De Stijl, Jay Hambidge, Irma Richter, the golden numberists, irrational numbers, logarithmic spiral, ratio and proportion, geometric art of M.C. Escher, Buckminster Fuller, Le Corbusier, geodesic domes, ratio and proportion, polyhedral, real landscapes, Mandelbrot, self-similarity, fractal art, randomness in art. References: 1. Paul Calter, Squaring the circle: geometry in art and architecture, 4th edition, Wiley, 2008. 2. Brunes, Tons, The Secrets of Ancient Geometry - and its use. Copenhagen. Rhodos, 1967. 3. Janson, H. W. History of Art. 5th Edition. NY: Abrams, 1995. 4. Lawlor, Robert. Sacred Geometry. NY: Thames & Hudson, 1982. .

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Painting by the Numbers: a Porter Postscript
Painting by the Numbers: A Porter Postscript Chris Bartlett Art Department Towson University 8000 York Road Towson, MD, 21252, USA. E-mail: [email protected] Abstract At the 2005 Bridges conference the author presented a paper titled, “Fairfield Porter’s Secret Geometry”. Porter (1907-1975), an important American painter, is known for his “naturalness” and seems to eschew any system of proportioning. This paper briefly traces other influences on Porter’s use of geometry in art and offers an analysis of two more of his paintings to reveal detailed and sophisticated geometric structures based on the Golden Ratio and Dynamic Symmetry. Introduction Artists throughout history have sought a key to beauty in proportioning systems in composition, a procedural method for compositional structure. Starting in the late 19th century there was a general resurgence of interest in geometrical structure as a basis for painting. Artists were researching aids to producing analogous and self-similar areas and repetitions of ratios in assigning the elements of a painting. In the 1920’s in America compositional methods gained new popularity fueled by Matila Ghyka and Jay Hambidge such that Milton Brown was prompted to title a critical article in the Magazine of Art, “Twentieth Century Nostrums: Pseudo-Scientific Theory in American Painting”. [1] More recently there have been growing circles criticizing the hegemony of the Golden Mean as a universal aesthetic panacea. [2] The principle of beauty underlining the application of the Golden Ratio and Dynamic Symmetry proportioning in a composition is not irrefutable, but what seems like a more useful exercise than to debate research in perception of elegant proportion is to look at the works of artists who seem to have fallen under its spell.
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Influences of the Ideas of Jay Hambidge on Art and Design
Computers Math. Appltc. Vol. 17, No. 4-6, pp. 1001-1008, 1989 0097-4943/89 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright © 1989 Pergamon Press plc INFLUENCES OF THE IDEAS OF JAY HAMBIDGE ON ART AND DESIGN H. J. McWmNNm Department of Design, University of Maryland, College Park, MD 20742, U.S.A. AImtraet--The system of dynamic symmetry, as an approach to decision-making in design, by Jay Hambidge in the early 1920s had a strong influence on industrial design as well as upon the work of painters. This paper will review the design theories of Jay Hambidge and dynamic symmetry in terms of the use of proportions in design which are humanistically based upon the proportions of the human body. Recent research in the general area known as the golden section hypothesis will be reviewed as a means of justification not only for Hambidge's theory of proportions in design but as a validation for recent ideas in design, especially those of Robert Venturi. The paper will demonstrate the utility of studies from the behaviorial sciences for questions of design history as well as for present-day design theory and practice. The work of contemporary artists and designers will be shown to demonstrate that these ideas, the golden section and dynamic symmetry, while popular in the 1920s, have a renewed sense of relevance to current ideas and approaches in design theory. The influence upon industrial design, while it may not be clear as say the influence of dynamic symmetry or the work of Bellows or Rothko, is nevertheless also quite clear.
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Aesthetical Issues of Leonardo Da Vinci's and Pablo Picasso's
heritage Article Aesthetical Issues of Leonardo Da Vinci’s and Pablo Picasso’s Paintings with Stochastic Evaluation G.-Fivos Sargentis * , Panayiotis Dimitriadis and Demetris Koutsoyiannis Laboratory of Hydrology and Water Resources Development, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 9, 157 80 Zographou, Greece; [email protected] (P.D.); [email protected] (D.K.) * Correspondence: fi[email protected] Received: 7 April 2020; Accepted: 21 April 2020; Published: 25 April 2020 Abstract: A physical process is characterized as complex when it is difficult to analyze or explain in a simple way. The complexity within an art painting is expected to be high, possibly comparable to that of nature. Therefore, constructions of artists (e.g., paintings, music, literature, etc.) are expected to be also of high complexity since they are produced by numerous human (e.g., logic, instinct, emotions, etc.) and non-human (e.g., quality of paints, paper, tools, etc.) processes interacting with each other in a complex manner. The result of the interaction among various processes is not a white-noise behavior, but one where clusters of high or low values of quantified attributes appear in a non-predictive manner, thus highly increasing the uncertainty and the variability. In this work, we analyze stochastic patterns in terms of the dependence structure of art paintings of Da Vinci and Picasso with a stochastic 2D tool and investigate the similarities or differences among the artworks. Keywords: aesthetic of art paintings; stochastic analysis of images; Leonardo Da Vinci; Pablo Picasso 1. Introduction The meaning of beauty is linked to the evolution of human civilization, and the analysis of the connection between the observer and the beauty in art and nature has always been of high interest in both philosophy and science.
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John Sharp Spirals and the Golden Section
John Sharp Spirals and the Golden Section The author examines different types of spirals and their relationships to the Golden Section in order to provide the necessary background so that logic rather than intuition can be followed, correct value judgments be made, and new ideas can be developed. Introduction The Golden Section is a fascinating topic that continually generates new ideas. It also has a status that leads many people to assume its presence when it has no relation to a problem. It often forces a blindness to other alternatives when intuition is followed rather than logic. Mathematical inexperience may also be a cause of some of these problems. In the following, my aim is to fill in some gaps, so that correct value judgements may be made and to show how new ideas can be developed on the rich subject area of spirals and the Golden Section. Since this special issue of the NNJ is concerned with the Golden Section, I am not describing its properties unless appropriate. I shall use the symbol I to denote the Golden Section (I |1.61803 ). There are many aspects to Golden Section spirals, and much more could be written. The parts of this paper are meant to be read sequentially, and it is especially important to understand the different types of spirals in order that the following parts are seen in context. Part 1. Types of Spirals In order to understand different types of Golden Section spirals, it is necessary to be aware of the properties of different types of spirals. This section looks at spirals from that viewpoint.
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Toward How to Add an Aesthetic Image to Mathematics Education
TOWARD HOW TO ADD AN AESTHETIC IMAGE TO MATHEMATICS EDUCATION Paul Betts University of Winnipeg [email protected] Abstract: The goal of this paper is to suggest how an aesthetic image can be added to mathematics education. Calls for reform in mathematics education (e.g., National Council for Teachers of Mathematics, 1989, 2000) are premised on shifting teacher attention from an absolutist toward a social constructivist philosophy of mathematics and mathematics education. The goal of reform is success for all students of mathematics. In a previous paper, I used ideas from art education to suggest that success for all might be achieved by fostering an aesthetic image of mathematics (Betts & McNaughton, 2003). This paper continues the argument by shifting from questions of why to how. Introduction In 1989, the National Council of Teachers of Mathematics (NCTM) published an influential mathematics curriculum framework document (see National Council of Teachers of Mathematics, 1989) calling for reform in mathematics and success for all mathematics students. This call for reform is based on social constructivism as a philosophy of mathematics and mathematics education. Proponents of social constructivism, as a philosophy of mathematics, view mathematics as fallible, changing and a product of human endeavor (Ernest, 1998). For example, the genesis of mathematical knowledge is a continual cycle of conjecture and refutation, and deduction is not the logic of mathematical discovery (Lakatos, 1976). In other words, mathematical truths are socially constructed via a process of error correction. Social constructivsm as a philosophy of mathematics education is based on fostering opportunities for students to experience, discover, discuss and re-construct the socially negotiated nature of mathematics.
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An Annotated Bibliography of Books for Architecture and Mathematics
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Information to Users
INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9123572 Art and mathematics: Enhancing achievement through curricular design Winter, June Frances M., Ph.D. The American University, 1991 Copyri^t ©1991 by Winter, June Prances M.
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Miszellaneen Miscellanea
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Hateful Contraries: Studies in Literature and Criticism
University of Kentucky UKnowledge Comparative Literature Arts and Humanities 12-31-1965 Hateful Contraries: Studies in Literature and Criticism W. K. Wimsatt Yale University Click here to let us know how access to this document benefits ou.y Thanks to the University of Kentucky Libraries and the University Press of Kentucky, this book is freely available to current faculty, students, and staff at the University of Kentucky. Find other University of Kentucky Books at uknowledge.uky.edu/upk. For more information, please contact UKnowledge at [email protected]. Recommended Citation Wimsatt, W. K., "Hateful Contraries: Studies in Literature and Criticism" (1965). Comparative Literature. 9. https://uknowledge.uky.edu/upk_comparative_literature/9 Hateful Contraries This page intentionally left blank Hateful Contraries STUDIES IN LITERATURE AND CRITICISM By W. K. WIMSATT With an Essay on English Meter Written in Collaboration with Monroe C. Beardsley KENTUCKY PAPERBACKS UNIVERSITY OF KENTUCKY PRESS Lexington, 1966 Copyright© 1965 by the University of Kentucky Press Printed in the United States of America by the University of Kentucky Printing Division Library of Congress Catalog Card No. 65-11823 F. W. H. HUMANITATE INSIGNI DOCTOR! ET DUCTORI D. D. D. W. K. W. This page intentionally left blank ACKNOWLEDGMENT THE ESSAYS in criticism and critical history which compose this book were published (all but one), in their original versions, over a period of about twelve years, from 1950 to 1962. The first essay in the collection, "Horses of Wrath: Recent Critical Lessons," has been rewritten from parts of the fol lowing three: "Criticism Today: A Report from America," in Essays in Criticism, VI (January, 1956); "Poetic Tension: A Summary," in the New Scholasticism, XXXII (January, 1958); and "Horses of Wrath: Recent Critical Lessons," in Essays in Criticism, XII (January, 1962).
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Winter, 1985 '· Editor: to the Editor: J
THE St. o 'sReview I : ... ::: ............... ~--'~---1. ....... I ' ··.. I )·<·· ·.. : .. · _:.-·· •. - .• Winter, 1985 '· Editor: To the editor: J. Walter Sterling At the urging of alumni and col leagues, and with the co-operation of Mrs. Klein, I am undertaking to Poetry Editor: gather material for a brieflife ofjacob Richard Freis Klein. I shall be pleased to have documents, reminiscences, or other Editorial Assistant: memorabilia. Jason Walsh I would be particularly pleased to hear from alumni who were members Editorial Board: of his classes in his first years of Eva Brann teaching, especially his first seminar. S. Richard Freis, Alumni representative Wye J. Allanbrook Joe Sachs St. John's College Cary Stickney Curtis A. Wilson Unsolicited articles, storieS, and poems are welcome, but should be accom panied by a stamped, self-addressed envelope in each instance. Reasoned comments are also welcome. The St. John's Review (formerly The Col lege) is published by the Office of the Dean, St. John's College, Annapolis, Maryland 21404. Edwin J. Delattre, President, George Do'skow, Dean. Published thrice yearly, in the winter, spring, and summer. For those not on the distribution list, subscriptions: $12.00 yearly, $24.00 for two years, or $36.00 for three years, payable in ad vance. Address all correspondence to The St. John's Review, St.John's College, Annapolis, Maryland 21404. Volume XXXVI, Number 1 Winter, 1985 © 1985 St. John's College; All rights reserved. Reproduction in whole or in part without permission is prohibited. ISSN 0277-4720 Cover: A Black-Figured Amphora from the Boston Museum (Drawn, measured and analyzed by L.D.
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Aistarch-N.-1.Pdf
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