Anamorphic Experiences in 3D Space: Shadows, Projections and Other Optical Illusions
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Catoptric Anamorphosis on Free-Form Reflective Surfaces Francesco Di Paola, Pietro Pedone
7 / 2020 Catoptric Anamorphosis on Free-Form Reflective Surfaces Francesco Di Paola, Pietro Pedone Abstract The study focuses on the definition of a geometric methodology for the use of catoptric anamorphosis in contemporary architecture. The particular projective phenomenon is illustrated, showing typological-geometric properties, responding to mechanisms of light re- flection. It is pointed out that previous experience, over the centuries, employed the technique, relegating its realisation exclusively to reflecting devices realised by simple geometries, on a small scale and almost exclusively for convex mirrors. Wanting to extend the use of the projective phenomenon and experiment with the expressive potential on reflective surfaces of a complex geometric free-form nature, traditional geometric methods limit the design and prior control of the results, thus causing the desired effect to fail. Therefore, a generalisable methodological process of implementation is proposed, defined through the use of algorithmic-parametric procedures, for the determination of deformed images, describing possible subsequent developments. Keywords: anamorphosis, science of representation, generative algorithm, free-form, design. Introduction The study investigates the theme of anamorphosis, a 17th The resulting applications require mastery in the use of the century neologism, from the Greek ἀναμόρϕωσις “rifor- various techniques of the Science of Representation aimed mazione”, “reformation”, derivation of ἀναμορϕόω “to at the formulation of the rule for the “deformation” and form again”. “regeneration” of represented images [Di Paola, Inzerillo, It is an original and curious geometric procedure through Santagati 2016]. which it is possible to represent figures on surfaces, mak- There is a particular form of expression, in art and in eve- ing their projections comprehensible only if observed ryday life, of anamorphic optical illusions usually referred from a particular point of view, chosen in advance by the to as “ catoptric “ or “ specular “. -
An Artistic and Mathematical Look at the Work of Maurits Cornelis Escher
University of Northern Iowa UNI ScholarWorks Honors Program Theses Honors Program 2016 Tessellations: An artistic and mathematical look at the work of Maurits Cornelis Escher Emily E. Bachmeier University of Northern Iowa Let us know how access to this document benefits ouy Copyright ©2016 Emily E. Bachmeier Follow this and additional works at: https://scholarworks.uni.edu/hpt Part of the Harmonic Analysis and Representation Commons Recommended Citation Bachmeier, Emily E., "Tessellations: An artistic and mathematical look at the work of Maurits Cornelis Escher" (2016). Honors Program Theses. 204. https://scholarworks.uni.edu/hpt/204 This Open Access Honors Program Thesis is brought to you for free and open access by the Honors Program at UNI ScholarWorks. It has been accepted for inclusion in Honors Program Theses by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. Running head: TESSELLATIONS: THE WORK OF MAURITS CORNELIS ESCHER TESSELLATIONS: AN ARTISTIC AND MATHEMATICAL LOOK AT THE WORK OF MAURITS CORNELIS ESCHER A Thesis Submitted in Partial Fulfillment of the Requirements for the Designation University Honors Emily E. Bachmeier University of Northern Iowa May 2016 TESSELLATIONS : THE WORK OF MAURITS CORNELIS ESCHER This Study by: Emily Bachmeier Entitled: Tessellations: An Artistic and Mathematical Look at the Work of Maurits Cornelis Escher has been approved as meeting the thesis or project requirements for the Designation University Honors. ___________ ______________________________________________________________ Date Dr. Catherine Miller, Honors Thesis Advisor, Math Department ___________ ______________________________________________________________ Date Dr. Jessica Moon, Director, University Honors Program TESSELLATIONS : THE WORK OF MAURITS CORNELIS ESCHER 1 Introduction I first became interested in tessellations when my fifth grade mathematics teacher placed multiple shapes that would tessellate at the front of the room and we were allowed to pick one to use to create a tessellation. -
The Creative Act in the Dialogue Between Art and Mathematics
mathematics Article The Creative Act in the Dialogue between Art and Mathematics Andrés F. Arias-Alfonso 1,* and Camilo A. Franco 2,* 1 Facultad de Ciencias Sociales y Humanas, Universidad de Manizales, Manizales 170003, Colombia 2 Grupo de Investigación en Fenómenos de Superficie—Michael Polanyi, Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Medellín 050034, Colombia * Correspondence: [email protected] (A.F.A.-A.); [email protected] (C.A.F.) Abstract: This study was developed during 2018 and 2019, with 10th- and 11th-grade students from the Jose Maria Obando High School (Fredonia, Antioquia, Colombia) as the target population. Here, the “art as a method” was proposed, in which, after a diagnostic, three moments were developed to establish a dialogue between art and mathematics. The moments include Moment 1: introduction to art and mathematics as ways of doing art, Moment 2: collective experimentation, and Moment 3: re-signification of education as a model of experience. The methodology was derived from different mathematical-based theories, such as pendulum motion, centrifugal force, solar energy, and Chladni plates, allowing for the exploration of possibilities to new paths of knowledge from proposing the creative act. Likewise, the possibility of generating a broad vision of reality arose from the creative act, where understanding was reached from logical-emotional perspectives beyond the rational vision of science and its descriptions. Keywords: art; art as method; creative act; mathematics 1. Introduction Citation: Arias-Alfonso, A.F.; Franco, C.A. The Creative Act in the Dialogue There has always been a conception in the collective imagination concerning the between Art and Mathematics. -
Mathematics K Through 6
Building fun and creativity into standards-based learning Mathematics K through 6 Ron De Long, M.Ed. Janet B. McCracken, M.Ed. Elizabeth Willett, M.Ed. © 2007 Crayola, LLC Easton, PA 18044-0431 Acknowledgements Table of Contents This guide and the entire Crayola® Dream-Makers® series would not be possible without the expertise and tireless efforts Crayola Dream-Makers: Catalyst for Creativity! ....... 4 of Ron De Long, Jan McCracken, and Elizabeth Willett. Your passion for children, the arts, and creativity are inspiring. Thank you. Special thanks also to Alison Panik for her content-area expertise, writing, research, and curriculum develop- Lessons ment of this guide. Garden of Colorful Counting ....................................... 6 Set representation Crayola also gratefully acknowledges the teachers and students who tested the lessons in this guide: In the Face of Symmetry .............................................. 10 Analysis of symmetry Barbi Bailey-Smith, Little River Elementary School, Durham, NC Gee’s-o-metric Wisdom ................................................ 14 Geometric modeling Rob Bartoch, Sandy Plains Elementary School, Baltimore, MD Patterns of Love Beads ................................................. 18 Algebraic patterns Susan Bivona, Mount Prospect Elementary School, Basking Ridge, NJ A Bountiful Table—Fair-Share Fractions ...................... 22 Fractions Jennifer Braun, Oak Street Elementary School, Basking Ridge, NJ Barbara Calvo, Ocean Township Elementary School, Oakhurst, NJ Whimsical Charting and -
Mathematical Concepts Within the Artwork of Lewitt and Escher
A Thesis Presented to The Faculty of Alfred University More than Visual: Mathematical Concepts Within the Artwork of LeWitt and Escher by Kelsey Bennett In Partial Fulfillment of the requirements for the Alfred University Honors Program May 9, 2019 Under the Supervision of: Chair: Dr. Amanda Taylor Committee Members: Barbara Lattanzi John Hosford 1 Abstract The goal of this thesis is to demonstrate the relationship between mathematics and art. To do so, I have explored the work of two artists, M.C. Escher and Sol LeWitt. Though these artists approached the role of mathematics in their art in different ways, I have observed that each has employed mathematical concepts in order to create their rule-based artworks. The mathematical ideas which serve as the backbone of this thesis are illustrated by the artists' works and strengthen the bond be- tween the two subjects of art and math. My intention is to make these concepts accessible to all readers, regardless of their mathematical or artis- tic background, so that they may in turn gain a deeper understanding of the relationship between mathematics and art. To do so, we begin with a philosophical discussion of art and mathematics. Next, we will dissect and analyze various pieces of work by Sol LeWitt and M.C. Escher. As part of that process, we will also redesign or re-imagine some artistic pieces to further highlight mathematical concepts at play within the work of these artists. 1 Introduction What is art? The Merriam-Webster dictionary provides one definition of art as being \the conscious use of skill and creative imagination especially in the production of aesthetic object" ([1]). -
Muse® Teacher Guide: January 2020
Muse® Teacher Guide: September 2020 What Is Perfection? It may be a relief to discover that being “imperfect” has some advantages. This issue of MUSE explores how variation and diversity contribute to excellence. In a world where we are compelled to strive for excellence, the articles in this guide examine why the journey, rather than the destination, should be our primary focus. CONVERSATION QUESTION When can imperfection be extraordinary? TEACHING OBJECTIVES • Students will learn about the use of the golden In addition to supplemental materials ratio in art. • Students will learn why game developers avoid focused on core STEM skills, this perfection. flexible teaching tool offers • Students will learn how variations in biology can be the key to excellence. vocabulary-building activities, • Students will investigate number patterns utilizing questions for discussion, and cross- the Fibonacci sequence. • Students will compare and contrast the elements curricular activities. of a wide game with the elements of a deep game. • Students will examine the structure and function SELECTIONS of variations in the human body that contribute to • The Art of the Golden Ratio the extraordinary functioning. Expository Nonfiction, ~900L • Students will research examples of the golden • Good Gaming ratio in art history. Expository Nonfiction, ~1100L • Students will use mathematical concepts to express game preferences. • Perfectly Imperfect • Students will study additional examples of Expository Nonfiction, ~700L adaptation in the animal kingdom. U33T http://www.cricketmedia.com/classroom/Muse-magazine Muse® Teacher Guide: September 2020 The Art of the Golden Ratio ENGAGE pp. 20–22, Expository Nonfiction Conversation Question: When can imperfection be extraordinary? This article explores the use of mathematical concepts in art. -
Britain's Hottalent
Britain’s Hot Talent 2014/15 A handbook of UK venture capital innovation Editors Chris Etheridge Rory McDougall Managing Editor Tom Allchorne For additional information Tom Allchorne Email [email protected] 22 BVCA e: [email protected] w: bvca.co.uk Contents Introduction Foreword 4 Five facts about venture capital in the UK 5 Definitions of industry sectors 6 Company Profiles Chapter 1 Cleantech 7 Chapter 2 Digital & Consumer 17 Chapter 3 Finance & Business Support 47 Chapter 4 Information Technology 69 Chapter 5 Life Sciences 91 Chapter 6 Materials 105 Chapter 7 Media 113 Chapter 8 Medical 123 Chapter 9 Telecoms 145 Index Index by company name 158 Index by investor 163 Index by parliamentary constituency 180 e: [email protected] w: bvca.co.uk BVCA 3 Foreword Welcome to Britain’s Hot Talent 2014/15, the third edition of the BVCA handbook, showcasing a selection of this country’s most dynamic and cutting-edge young companies. Britain has a long and proud history of entrepreneurship and the businesses featured here present a snapshot of some of the exciting and creative work being carried out right now. This edition has profiles of over 100 venture-capital-backed companies from ten distinct sectors of the British economy, all fantastic examples of what can be achieved with ingenuity, hard work and the right support. Venture capital has long been a backer of innovative businesses, and such skills and investment are needed now more than ever before. As the UK recovers from the worst economic recession in over 50 years, it is vital that entrepreneurship is encouraged in all its forms and across all industries, from life sciences to finance, from digital media to online security. -
William Broadhead Professor of History Thesis Supervisor
Vitruvius on Architecture: A Modem Application and Stability Analysis of Classical Structures by Ana S. Escalante Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Mechanical Engineering at the Lj Massachusetts Institute of Technology June 2013 0 2013 Ana S. Escalante. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created Signature of Author: F , 2 I- - Department of Mechanical Engineering May 28, 2013 Certified by: William Broadhead Professor of History Thesis Supervisor Accepted by: Annette Hosoi Professor of Mechanical Engineering Undergraduate Officer 1 2 Vitruvius on Architecture: A Modem Application and Stability Analysis of Classical Structures by Ana S. Escalante Submitted to the Department of Mechanical Engineering on June 7, 2013 in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Mechanical Engineering ABSTRACT Imperial Rome has left numerous legacies, the most well-known being its literature and monuments. Though many monuments, such as the Pantheon, are well-preserved, in cases where little physical evidence remains, historians can often use literary sources to inform reconstruction efforts. For more technical studies of Roman construction, technical literature is rare and the contemporary awareness of such literature even less known. When Vitruvius wrote De architectura,he did not intend for it to be a manual for instruction but rather a central source of general architectural knowledge. Directly aimed at architects, contractors, and other individuals involved in the design and construction of buildings, De architecturaprovides insight into contemporary technical knowledge. -
Fictional Illustration Language with Reference to MC Escher and Istvan
New Trends and Issues Proceedings on Humanities and Social Sciences Volume 4, Issue 11, (2017) 156-163 ISSN : 2547-881 www.prosoc.eu Selected Paper of 6th World Conference on Design and Arts (WCDA 2017), 29 June – 01 July 2017, University of Zagreb, Zagreb – Croatia Fictional Illustration Language with Reference to M. C. Escher and Istvan Orosz Examples Banu Bulduk Turkmen a*, Faculty of Fine Arts, Department of Graphics, Hacettepe University, Ankara 06800, Turkey Suggested Citation: Turkmen, B. B. (2017). Fictional illustration language with reference to M. C. Escher and Istvan Orosz examples. New Trends and Issues Proceedings on Humanities and Social Sciences. [Online]. 4(11), 156-163. Available from: www.prosoc.eu Selection and peer review under responsibility of Prof. Dr. Ayse Cakır Ilhan, Ankara University, Turkey. ©2017 SciencePark Research, Organization & Counseling. All rights reserved. Abstract Alternative approaches in illustration language have constantly been developing in terms of material and technical aspects. Illustration languages also differ in terms of semantics and form. Differences in formal expressions for increasing the effect of the subject on the audience lead to diversity in the illustrations. M. C. Escher’s three-dimensional images to be perceived in a two-dimensional environment, together with mathematical and symmetry-oriented studies and the systematic formed by a numerical structure in its background, are associated with the notion of illustration in terms of fictional meaning. Istvan Orosz used the technique of anamorphosis and made it possible for people to see their perception abilities and visual perception sensitivities in different environments created by him. This study identifies new approaches and illustration languages based on the works of both artists, bringing an alternative proposition to illustration languages in terms of systematic sub-structure and fictional idea sketches. -
A Mathematician's Lament
A Mathematician’s Lament by Paul Lockhart musician wakes from a terrible nightmare. In his dream he finds himself in a society where A music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer. Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school. As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. -
'The Hurwitz Singularity'
‘The Hurwitz Singularity’ “In a moment of self-doubt in 2003, (Portrait of Edward VI, 1546) I rushed I wondered into the National Portrait home and within hours was devouring Gallery and tumbled across a strange the works of Escher, Da Vinci and many anamorphic piece by William Scrots more. In a breath I had found ‘brothers’.” 2 The art of anamorphic perspective. Not being the only one perspective has been to admire Hurwitz’s work, Colossal present, in the world of art, Magazine identified that ‘some Tsince the great Leonardo figurative sculptors carve their Da Vinci. It can be said that Da Vinci artworks from unforgiving stone, was the first artist to use anamorphic while others carefully morph the perspective, within the arts, followed human form from soft blocks of clay. by legends such as Hans Holbein Artist Jonty Hurwitz begins with over and Andreas Pozzo, who also used a billion computer calculations before anamorphic perspective within their spending months considering how to art. The two principal techniques materialize his warped ideas using of Anamorphosis are ‘perspective perspex, steel, resin, or copper.’[3] (oblique) and mirror (catoptric).’ [1] The Technique that I will be discussing is most familiar to relate to oblique Anamorphosis. It can be created using Graphic design techniques of perspective and using innovative print and precise design strategies. My first interest in anamorphic perspective was when producing an entry for the ‘Design Museum; 2014 Competition brief: Surprise.’[2] The theme of Surprise led me to discover the astonishment that viewers of anamorphic perspective art felt. Artists such as Jonty Hurwitz, joseph Egan and hunter Thomson; all of which are recognised for their modern approach to Anamorphosis, also created this amazement with their art. -
Rule Technische Universiteit
( Technische Universiteit Eindhoven rUle University of Technolog Path of life in mixed reality Proposed by: Prof. G.W.M. Rauterberg September 2012 - June 2013 By Kiarash Irandoust [email protected] Coach: Lucian Reindl, ©K. Irandoust 2013 2 This report is a brief overview of my master graduation project "Path of life in It is worth mentioning that the information and knowledge that I gained in this mixed reality"; a project which intends to create an interactive installation that stage are the foundation of the final design. enable visitors to experience deeply rooted cultural dimensions based on seven My reason for choosing this topic was due to my vision on creating societal stages in life. i The design challenge is drawing on results from different disci changes and the responsibility that I feel as a designer. My intension was to in plines: religion, sociology, design, and engineering sciences 1. form people and invite them to re-think about issues which are inseparable part of our life and consciously/unconsciously have a great impact on our life. I started this project by looking at various definitions of culture. What is cul ture? And how does culture manifest itself in life? Subsequently, I looked at the Second iteration, conceptualization and validation: the conceptualization pro meaning of life; what does life mean? And how do different cultures look at life cess was through idea generation and model making. It was an iterative process (seven stages of life). Furthermore, I looked at the concept of death from differ in which the final concept shaped gradually.