Use of Mathematics in Art
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Feasibility Study for Teaching Geometry and Other Topics Using Three-Dimensional Printers
Feasibility Study For Teaching Geometry and Other Topics Using Three-Dimensional Printers Elizabeth Ann Slavkovsky A Thesis in the Field of Mathematics for Teaching for the Degree of Master of Liberal Arts in Extension Studies Harvard University October 2012 Abstract Since 2003, 3D printer technology has shown explosive growth, and has become significantly less expensive and more available. 3D printers at a hobbyist level are available for as little as $550, putting them in reach of individuals and schools. In addition, there are many “pay by the part” 3D printing services available to anyone who can design in three dimensions. 3D graphics programs are also widely available; where 10 years ago few could afford the technology to design in three dimensions, now anyone with a computer can download Google SketchUp or Blender for free. Many jobs now require more 3D skills, including medical, mining, video game design, and countless other fields. Because of this, the 3D printer has found its way into the classroom, particularly for STEM (science, technology, engineering, and math) programs in all grade levels. However, most of these programs focus mainly on the design and engineering possibilities for students. This thesis project was to explore the difficulty and benefits of the technology in the mathematics classroom. For this thesis project we researched the technology available and purchased a hobby-level 3D printer to see how well it might work for someone without extensive technology background. We sent designed parts away. In addition, we tried out Google SketchUp, Blender, Mathematica, and other programs for designing parts. We came up with several lessons and demos around the printer design. -
Oral History Interview with Nicholas Krushenick, 1968 Mar. 7-14
Oral history interview with Nicholas Krushenick, 1968 Mar. 7-14 Contact Information Reference Department Archives of American Art Smithsonian Institution Washington. D.C. 20560 www.aaa.si.edu/askus Transcript Preface The following oral history transcript is the result of a tape-recorded interview with Nicholas Krushenick on March 7, 1968. The interview was conducted in New York by Paul Cummings for the Archives of American Art, Smithsonian Institution. Interview PAUL CUMMINGS: This is March 7, 1968. Paul Cummings talking to Nicholas Krushenick. You’re a rare born New Yorker? NICHOLAS KRUSHENICK: Yes. One of the last. PAUL CUMMINGS: Let’s see, May 31, 1929. NICHOLAS KRUSHENICK: Very Young. PAUL CUMMINGS: That’s the year to do it. NICHOLAS KRUSHENICK: That’s the year of the zero, the crash. PAUL CUMMINGS: Well, why don’t you tell me something about your family, what part of New York you were born in. NICHOLAS KRUSHENICK: I was born up in the Bronx in a quiet little residential neighborhood. Luckily enough my father actually brought me into the world. The doctor didn’t get there soon enough and my father did the operation himself; he ties the knot and the whole thing. When the doctor got there he said it was a beautiful job. And I went to various public schools in the Bronx. PAUL CUMMINGS: You have what? –one brother? More brothers? Any sisters? NICHOLAS KRUSHENICK: Just one brother. PAUL CUMMINGS: What did you live in – a house? Or an apartment? NICHOLAS KRUSHENICK: No. Actually it was the Depression days. And we were the superintendents of a building. -
Fall 201720172017
2017 2017 2017 2017 Fall Fall Fall Fall This content downloaded from 024.136.113.202 on December 13, 2017 10:53:41 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). American Art SummerFall 2017 2017 • 31/3 • 31/2 University of Chicago Press $20 $20 $20 $20 USA USA USA USA 1073-9300(201723)31:3;1-T 1073-9300(201723)31:3;1-T 1073-9300(201723)31:3;1-T 1073-9300(201723)31:3;1-T reform reform reform reform cameras cameras cameras cameras “prints” “prints” “prints” “prints” and and and and memory memory memory memory playground playground playground playground of of of Kent’s of Kent’s Kent’s Kent’s guns, guns, guns, guns, abolitionism abolitionism abolitionism abolitionism art art art art and and and and the the the the Rockwell literary Rockwell Rockwell literary literary Rockwell issue literary issue issue issue Group, and Group, and Group, and Group, and in in in in this this this this Homer—dogs, Homer—dogs, Homer—dogs, Place Homer—dogs, Place Place Place In In In In nostalgia Park nostalgia nostalgia Park Park nostalgia Park Duncanson’s Duncanson’s Duncanson’s Duncanson’s Christenberry the Christenberry S. Christenberry the S. the S. Christenberry the S. Winslow Winslow Winslow Winslow with with with with Robert Robert Robert Robert Suvero, Suvero, Suvero, Suvero, William William William William di di di Technological di Technological Technological Technological Hunting Hunting Hunting Hunting Mark Mark Mark Mark Kinetics of Liberation in Mark di Suvero’s Play Sculpture Melissa Ragain Let’s begin with a typical comparison of a wood construction by Mark di Suvero with one of Tony Smith’s solitary cubes (fgs. -
Metaphysical Mathematics 111
JOLE DE SANNA: METAPHYSICAL MATHEMATICS 111 METAPHYSICAL MATHEMATICS Jole de Sanna The metaphysical act imposes an identity that requires a terminology deal- ing with opposites. Dedicated to the geometric functions of metaphysical painting, the following study demonstrates how, from two extremities of history, Pythagorean harmony and modern mathematical physics come together in de Chirico’s work, upholding the space of the painting. At the dawn of the last century, for the young “Faust” descendants of Goethe, space was the valet of time. In 1906, de Chirico and his adoles- cent peers in Munich enclosed interiority and psychic flow inside “time”. Oswald Spengler writes that “one’s own”, destiny and time are mutable terms.1 De Chirico appropriates the perception of cosmic rhythm as a “voyager in time and within himself”. In the paintings, the natural science of the past – Pythagorean harmony – reaches the frontiers of modern physics in a unity of time constituted as “one’s own”. With fixed attention on “his” epoch, the artist superimposes two different phases of history and visions of the universe. At the beginning of the twentieth century, the concentration of energy focused on art was parallel to the expansion of mathematics and theoretical physics. To the trained eye, the connection between these endeavours is evident. The paintings analysed here trace out a genealogy of space in this order: • the fulfilment of harmony and the Golden Ratio in a Pythagorean and Platonic context (from Timaeus) in the first metaphysical paintings (1910- 12) situated in relation to the Universe or Infinite, as well as the rediscov- ery of the scenography of Ancient Rome and the use of modern theatre technology to define the metaphysical piazza (town square) inside the uniform polyhedron; 1 O. -
Art Curriculum 1
Ogdensburg School Visual Arts Curriculum Adopted 2/23/10 Revised 5/1/12, Born on: 11/3/15, Revised 2017 , Adopted December 4, 2018 Rationale Grades K – 8 By encouraging creativity and personal expression, the Ogdensburg School District provides students in grades one to eight with a visual arts experience that facilitates personal, intellectual, social, and human growth. The Visual Arts Curriculum is structured as a discipline based art education program aligned with both the National Visual Arts Standards and the New Jersey Core Curriculum Content Standards for the Visual and Performing Arts. Students will increase their understanding of the creative process, the history of arts and culture, performance, aesthetic awareness, and critique methodologies. The arts are deeply embedded in our lives shaping our daily experiences. The arts challenge old perspectives while connecting each new generation from those in the past. They have served as a visual means of communication which have described, defined, and deepened our experiences. An education in the arts fosters a learning community that demonstrates an understanding of the elements and principles that promote creation, the influence of the visual arts throughout history and across cultures, the technologies appropriate for creating, the study of aesthetics, and critique methodologies. The arts are a valuable tool that enhances learning st across all disciplines, augments the quality of life, and possesses technical skills essential in the 21 century. The arts serve as a visual means of communication. Through the arts, students have the ability to express feelings and ideas contributing to the healthy development of children’s minds. These unique forms of expression and communication encourage students into various ways of thinking and understanding. -
Robert Morris, Minimalism, and the 1960S
City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 1988 The Politics of Experience: Robert Morris, Minimalism, and the 1960s Maurice Berger Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/1646 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] INFORMATION TO USERS The most advanced technology has been used to photograph and reproduce this manuscript 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. -
Pdf 107.05 K
ISSN: 1017-060X (Print) ISSN: 1735-8515 (Online) Special Issue of the Bulletin of the Iranian Mathematical Society in Honor of Professor Heydar Radjavi's 80th Birthday Vol. 41 (2015), No. 7, pp. 99{106 . Title: A Haar wavelets approach to Stirling's formula Author(s): M. Ahmadinia and H. Naderi Yeganeh Published by Iranian Mathematical Society http://bims.ims.ir Bull. Iranian Math. Soc. Vol. 41 (2015), No. 7, pp. 99{106 Online ISSN: 1735-8515 A HAAR WAVELETS APPROACH TO STIRLING'S FORMULA M. AHMADINIA∗ AND H. NADERI YEGANEH (Communicated by Peter Rosenthal) Dedicated to Professor Heydar Radjavi on his 80th birthday Abstract. This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences. Keywords: Haar wavelets, Parseval's identity, Stirling's formula. MSC(2010): Primary: 15-xx; Secondary: 40-xx. 1. Introduction n! Stirling's formula (lim !1 p = 1) plays an important role in statis- n nne−n 2πn tics and probability; its main use is estimating the value of n!. The first proofs of Stirling's formula were presented by de Moivre and Stirling (see [4, 8]). Es- timates of n! have been obtained via upper and lower bounds of n! by various authors (for example see [3], [5] and [6]). Some papers prove Stirling's formula by different techniques as well (for example see [2]). The present paper in- troduces a new method of proving Stirling's formula by using Haar wavelets. -
LOCKDOWN Maths Inspired Art No Longer an Etching but a Multi Medium Artwork A3 Size
LOCKDOWN Maths Inspired Art No Longer an Etching but a Multi Medium Artwork A3 size Gr11 /// PMM /// Term 2 /// 2020 Term 2’s theme has been inspired by the http://www.mathart.co.za/ competition initiated by the education department. We want to explore the link between making art and understanding maths principles. Each learner is to find a connection between a visual composition and being able to explain this using a mathematical explanation. Patterns, tessellations, fractals, proportion and perspective are all themes one could explore in this term 2 project. I suggest learners keep their final compositions simple and clean. Simple black line work as we are producing hard ground etchings in class. Due to the lockdown situation I would like each learner to produce their final practical at home. We will stick to the same theme as you have all done much work in your SB. What I would like is a final artwork, No smaller than A3 in whatever and whichever materials you have in your space at home. Please don't forget that stationary shops including art shops are open. I understand money is tight however pens, pencils, food colouring, coffee we should be able to work with easier. You will take your final composition and produce a final artwork with your ideas and creativity around “Maths in Art”. Suggestions for paper - cardboard boxes, old cereal boxes, collaging paper together. Please explore the format of the canvas - square, rectangular, oval are all options. [Each learn has already been given a brass etching plate and therefore has the size (39com x18cm) of the final composition. -
The Mazzocchio in Perspective
Bridges 2011: Mathematics, Music, Art, Architecture, Culture The Mazzocchio in Perspective Kenneth Brecher Departments of Astronomy and Physics Boston University Boston, MA 02215, U.S.A. E-mail: [email protected] Abstract The mazzocchio was a part of 15th century Italian headgear. It was also a kind of final exam problem for students of perspective. Painted by Uccello, drawn by Leonardo, incorporated into intarsia and prints through the 16th century, it still appears occasionally in 21st century art. Here we review its history; show 3D models made by hand in wood and using stereolithography in plastic; and report two novel visual effects seen when viewing the 3D models. Brief History of the Mazzocchio in Paintings and in Graphics The origins of the kind of geometrical mazzocchios discussed in this paper are obscure. They are said to derive from supports for headgear worn in Renaissance Italy during the 15th century. No actual three- dimensional examples survive from that period. Mazzocchios are featured in three major paintings by Paolo Uccello made between 1456 and 1460 and in his fresco of “The Flood” (Figure 1a). Leonardo Da Vinci also illustrated them and may have built models of the skeletal version in the late 15th century (cf. Figure 2a). Whether the wooden “checkerboard” version was actually worn on the head or around the neck is unclear. It seems more likely that a fabric version could have actually functioned as a headpiece. Figures 1 a (l.) & b (r.): (a) Detail from the fresco in Florence “The Flood and Waters Subsiding” by Paolo Uccello (ca. 1448) and (b) a pen and ink perspective study of a mazzocchio by Paolo Uccello (in the Louvre, Paris). -
(Lot of 6) 1966 Chateau Petit-Village Pomerol, Each 750Ml $ 300 - 500 2001 (Lot of 5) 1966 Chateau Petit-Village Pomerol, Each 750Ml $ 300 - 500
LOW HIGH Lot Description Estimate Estimate 2000 (lot of 6) 1966 Chateau Petit-Village Pomerol, each 750ml $ 300 - 500 2001 (lot of 5) 1966 Chateau Petit-Village Pomerol, each 750ml $ 300 - 500 2002 (lot of 3) French wine group, consisting of a 1970 Domaine Dujac Bonnes-Mares; and (2) 1969 Louis Latour Savigny-les-Beaune Cote de Beaune, each 750ml $ 400 - 600 (lot of 3) French wine group, consisting of a 1959 Chateau Rauzan-Gassies, Margaux; a 2003 1967 Armand Roux Bonnes-Mares; and a 1970 Maison Albert Brenot Bourgogne, each 750ml $ 500 - 700 (lot of 8) French wine group, consisting of a 1967 and (7) 1969 Chateau de la Gardine 2004 Chateauneuf-du-Pape, Rhone, each 750ml $ 400 - 600 (lot of 7) French wine group, consisting of a 1967 and (6) 1969 Chateau de la Gardine 2005 Chateauneuf-du-Pape, Rhone, each 750ml $ 400 - 600 2006 (lot of 15) 1964 Chateau de la Tour Clos-Vougeot, each 750 ml $ 300 - 500 2007 (lot of 18) 1964 Chateau de la Tour Clos-Vougeot, each 750 ml $ 300 - 500 1996 Domaine Drouhin Pinot Noir, Laurène, Oregon, 1.5l. Provenance: From the Ligonier, 2008 PA estate of Richard Mellon Scaife $ 100 - 200 (lot of 17) French, German and California wine group, consisting of (9) NV Tattinger Brut La Francaise; (4) 1969 Robert Mondavi; (3) 1966 Kesselstatt Josephshofer Riesling 2009 Spatlese; 1966 Chateau Moncontour Vouvray Demi-Sec; and a 1971 Grunhauser, each 750ml $ 300 - 500 2010 (lot of 6) 1964 Chateau Bellegrave Gran Vin, Pauillac, each 750ml $ 600 - 900 (lot of 8) French wine group consisting of a 1962 and (7) 1964 Chateau Bellegrave Gran 2011 Vin, Pauillac, each 750ml $ 500 - 700 (lot of 6) French wine group consisting of (2) 1966 Chateau Beychevelle Grand Vin, Saint- 2012 Julien; and (4) 1971 Tytell Europa St. -
Piero Della Francesca
the cambridge companion to Piero della Francesca Edited by Jeryldene M. Wood University ofIllinois, Urbana-Champaign published by the press syndicate of the university of cambridge The Pitt Building, Trumpington Street, Cambridge, United Kingdom cambridge university press The Edinburgh Building, Cambridge cb2 2ru,UK 40 West 20th Street, New York, ny 10011–4211, USA 477 Williamstown Road, Port Melbourne, vic 3207, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 2002 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2002 Printed in the United Kingdom at the University Press, Cambridge Typeface Fairfield Medium 10.5/13 pt. System QuarkXPress® [GH] A catalog record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data The Cambridge companion to Piero della Francesca / edited by Jeryldene M. Wood. p. cm. – (Cambridge companions to the history of art) Includes bibliographical references and index. isbn 0-521-65254-5 – ISBN 0-521-65472-6 (pbk.) 1. Piero, della Francesca, 1416?–1492 – Criticism and interpretation. 2.Art, Renaissance – Italy. 3. Art, Italian – 15th century. I. Wood, Jeryldene. II. Series. ND623.F78 C26 2002 759.5 – dc21 2001043485 isbn 0 521 65254 5 hardback isbn 0 521 65472 6 paperback I. Encyclopedias and dictionaries ag5.c26 1990 031-dc20 isbn 0 521 39538 3 hardback isbn 0 521 39539 3 paperback Contents List of Illustrations page vii Acknowledgments xiii Contributors xv Introduction 1 Jeryldene M. -
PROJECT DESCRIPTIONS — MATHCAMP 2016 Contents Assaf's
PROJECT DESCRIPTIONS | MATHCAMP 2016 Contents Assaf's Projects 2 Board Game Design/Analysis 2 Covering Spaces 2 Differential Geometry 3 Chris's Projects 3 Π1 of Campus 3 Don's Projects 3 Analytics of Football Drafts 3 Open Problems in Knowledge Puzzles 4 Finite Topological Spaces 4 David's Projects 4 p-adics in Sage 4 Gloria's Projects 5 Mathematical Crochet and Knitting 5 Jackie's Projects 5 Hanabi AI 5 Jane's Projects 6 Art Gallery Problems 6 Fractal Art 6 Jeff's Projects 6 Building a Radio 6 Games with Graphs 7 Lines and Knots 7 Knots in the Campus 7 Cities and Graphs 8 Mark's Projects 8 Knight's Tours 8 Period of the Fibonacci sequence modulo n 9 Misha's Projects 9 How to Write a Cryptic Crossword 9 How to Write an Olympiad Problem 10 Nic's Projects 10 Algebraic Geometry Reading Group 10 1 MC2016 ◦ Project Descriptions 2 Ray Tracing 10 Non-Euclidean Video Games 11 Nic + Chris's Projects 11 Non-Euclidean Video Games 11 Pesto's Projects 11 Graph Minors Research 11 Linguistics Problem Writing 12 Models of Computation Similar to Programming 12 Sachi's Projects 13 Arduino 13 Sam's Projects 13 History of Math 13 Modellin' Stuff (Statistically!) 13 Reading Cauchy's Cours d'Analyse 13 Zach's Projects 14 Build a Geometric Sculpture 14 Design an Origami Model 14 Assaf's Projects Board Game Design/Analysis. (Assaf) Description: I'd like to think about and design a board game or a card game that has interesting math, but can still be played by a non-mathematician.