HYPERSEEING the Publication of the International Society of the Arts, Mathematics, and Architecture Spring 2009
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
The Mathematics of Fels Sculptures
THE MATHEMATICS OF FELS SCULPTURES DAVID FELS AND ANGELO B. MINGARELLI Abstract. We give a purely mathematical interpretation and construction of sculptures rendered by one of the authors, known herein as Fels sculptures. We also show that the mathematical framework underlying Ferguson's sculpture, The Ariadne Torus, may be considered a special case of the more general constructions presented here. More general discussions are also presented about the creation of such sculptures whether they be virtual or in higher dimensional space. Introduction Sculptors manifest ideas as material objects. We use a system wherein an idea is symbolized as a solid, governed by a set of rules, such that the sculpture is the expressed material result of applying rules to symbols. The underlying set of rules, being mathematical in nature, may thus lead to enormous abstraction and although sculptures are generally thought of as three dimensional objects, they can be created in four and higher dimensional (unseen) spaces with various projections leading to new and pleasant three dimensional sculptures. The interplay of mathematics and the arts has, of course, a very long and old history and we cannot begin to elaborate on this matter here. Recently however, the problem of creating mathematical programs for the construction of ribbed sculptures by Charles Perry was considered in [3]. For an insightful paper on topological tori leading to abstract art see also [5]. Spiral and twirling sculptures were analysed and constructed in [1]. This paper deals with a technique for sculpting works mostly based on wood (but not necessarily restricted to it) using abstract ideas based on twirls and tori, though again, not limited to them. -
Sculptures in S3
Sculptures in S3 Saul Schleimer and Henry Segerman∗ Abstract We describe the construction of a number of sculptures. Each is based on a geometric design native to the three- sphere: the unit sphere in four-dimensional space. Via stereographic projection, we transfer the design to three- dimensional space. All of the sculptures are then fabricated by the 3D printing service Shapeways. 1 Introduction The three-sphere, denoted S3, is a three-dimensional analog of the ordinary two-dimensional sphere, S2. In n+ general, the n–dimensional sphere is a subset of R 1 as follows: n n+1 2 2 2 S = f(x0;x1;:::;xn) 2 R j x0 + x1 + ··· + xn = 1g: Thus S2 can be seen as the usual unit sphere in R3. Visualising objects in dimensions higher than three is non-trivial. However for S3 we can use stereographic projection to reduce the dimension from four to three. n n n Let N = (0;:::;0;1) be the north pole of S . We define stereographic projection r : S − fNg ! R by x0 x1 xn−1 r(x0;x1;:::;xn) = ; ;:::; : 1 − xn 1 − xn 1 − xn See [1, page 27]. Figure 1a displays the one-dimensional case; this is also a cross-section of the n– dimensional case. For any point (x;y) 2 S1 − fNg draw the straight line L between N and (x;y). Then L meets R1 at a single point; this is r(x;y). N x 1−y (x;y) (a) Stereographic projection from S1 − (b) Two-dimensional stereographic projection applied to the Earth. -
The Mathematics of Mitering and Its Artful Application
The Mathematics of Mitering and Its Artful Application Tom Verhoeff Koos Verhoeff Faculty of Mathematics and CS Valkenswaard, Netherlands Eindhoven University of Technology Den Dolech 2 5612 AZ Eindhoven, Netherlands Email: [email protected] Abstract We give a systematic presentation of the mathematics behind the classic miter joint and variants, like the skew miter joint and the (skew) fold joint. The latter is especially useful for connecting strips at an angle. We also address the problems that arise from constructing a closed 3D path from beams by using miter joints all the way round. We illustrate the possibilities with artwork making use of various miter joints. 1 Introduction The miter joint is well-known in the Arts, if only as a way of making fine frames for pictures and paintings. In its everyday application, a common problem with miter joints occurs when cutting a baseboard for walls meeting at an angle other than exactly 90 degrees. However, there is much more to the miter joint than meets the eye. In this paper, we will explore variations and related mathematical challenges, and show some artwork that this provoked. In Section 2 we introduce the problem domain and its terminology. A systematic mathematical treatment is presented in Section 3. Section 4 shows some artwork based on various miter joints. We conclude the paper in Section 5 with some pointers to further work. 2 Problem Domain and Terminology We will now describe how we encountered new problems related to the miter joint. To avoid misunderstand- ings, we first introduce some terminology. Figure 1: Polygon knot with six edges (left) and thickened with circular cylinders (right) 225 2.1 Cylinders, single and double beveling, planar and spatial mitering Let K be a one-dimensional curve in space, having finite length. -
Cross-Section- Surface Area of a Prism- Surface Area of a Cylinder- Volume of a Prism
S8.6 Volume Things to Learn (Key words, Notation & Formulae) Complete from your notes Radius- Diameter- Surface Area- Volume- Capacity- Prism- Cross-section- Surface area of a prism- Surface area of a cylinder- Volume of a prism- Section 1. Surface area of cuboids: Q1. Work out the surface area of each cuboid shown below: Q2. What is the surface area of a cuboid with the dimensions 4cm, 5cm and 6cm? Section 2. Volume of cuboids: Q1. Calculate the volume of these cuboids: S8.6 Volume Q2. Section 3. Definition of prisms: Label all the shapes and tick the ones that are prisms. Section 4. Surface area of prisms: Q1. Find the surface area of this triangular prism. Q2. Calculate the surface area of this cylinder. S8.6 Volume Q3. Cans are in cylindrical shapes. Each can has a diameter of 5.3 cm and a height of 11.4 cm. How much paper is required to make the label for the 20 cans? Section 5. Volume of a prism: Q1. Find the volume of this L-shaped prism. Q2. Calculate the volume of this prism. Give your answer to 2sf Section 6 . Volume of a cylinder: Q1. Calculate the volume of this cylinder. S8.6 Volume Q2. The diagram shows a piece of wood. The piece of wood is a prism of length 350cm. The cross-section of the prism is a semi-circle with diameter 1.2cm. Calculate the volume of the piece of wood. Give your answer to 3sf. Section 7. Problems involving volume and capacity: Q1. Sam buys a planter shown below. -
Calculus Terminology
AP Calculus BC Calculus Terminology Absolute Convergence Asymptote Continued Sum Absolute Maximum Average Rate of Change Continuous Function Absolute Minimum Average Value of a Function Continuously Differentiable Function Absolutely Convergent Axis of Rotation Converge Acceleration Boundary Value Problem Converge Absolutely Alternating Series Bounded Function Converge Conditionally Alternating Series Remainder Bounded Sequence Convergence Tests Alternating Series Test Bounds of Integration Convergent Sequence Analytic Methods Calculus Convergent Series Annulus Cartesian Form Critical Number Antiderivative of a Function Cavalieri’s Principle Critical Point Approximation by Differentials Center of Mass Formula Critical Value Arc Length of a Curve Centroid Curly d Area below a Curve Chain Rule Curve Area between Curves Comparison Test Curve Sketching Area of an Ellipse Concave Cusp Area of a Parabolic Segment Concave Down Cylindrical Shell Method Area under a Curve Concave Up Decreasing Function Area Using Parametric Equations Conditional Convergence Definite Integral Area Using Polar Coordinates Constant Term Definite Integral Rules Degenerate Divergent Series Function Operations Del Operator e Fundamental Theorem of Calculus Deleted Neighborhood Ellipsoid GLB Derivative End Behavior Global Maximum Derivative of a Power Series Essential Discontinuity Global Minimum Derivative Rules Explicit Differentiation Golden Spiral Difference Quotient Explicit Function Graphic Methods Differentiable Exponential Decay Greatest Lower Bound Differential -
THIAGO JOSÉ CÓSER Possibilidades Da Produção Artística Via
THIAGO JOSÉ CÓSER Possibilidades da produção artística via prototipagem rápida: processos CAD/CAM na elaboração e confecção de obras de arte e o vislumbre de um percurso poético individualizado neste ensaio. Dissertação apresentada ao Instituto de Artes da Universidade Estadual de Campinas, para a obtenção do título de mestre em Artes. Área de concentração: Artes Visuais Orientador: Prof. Dr. Marco Antonio Alves do Valle Campinas 2010 3 FICHA CATALOGRÁFICA ELABORADA PELA BIBLIOTECA DO INSTITUTO DE ARTES DA UNICAMP Cóser, Thiago José. C89p Possibilidades da produção artística via Prototipagem Rápida: Processos CAD/CAM na elaboração e confecção de obras de arte e o vislumbre de um percurso poético individualizado neste ensaio. : Thiago José Cóser. – Campinas, SP: [s.n.], 2010. Orientador: Prof. Dr. Marco Antonio Alves do Valle. Dissertação(mestrado) - Universidade Estadual de Campinas, Instituto de Artes. 1. Prototipagem rápida. 2. Arte. 3. Sistema CAD/CAM. 4. Modelagem 3D. 5. escultura. I. Valle, Marco Antonio Alves do. II. Universidade Estadual de Campinas. Instituto de Artes. III. Título. (em/ia) Título em inglês: “Possibilities of Art via Rapid Prototyping: using CAD / CAM systems to create art works and a glimpse of a poetic route individualized essay.” Palavras-chave em inglês (Keywords): Rapid prototyping ; Art ; CAD/CAM systems. ; 3D modelling ; Sculpture. Titulação: Mestre em Artes. Banca examinadora: Prof. Dr. Marco Antonio Alves do Valle. Profª. Drª. Sylvia Helena Furegatti. Prof. Dr. Francisco Borges Filho. Prof. Dr. Carlos Roberto Fernandes. (suplente) Prof. Dr. José Mario De Martino. (suplente) Data da Defesa: 26-02-2010 Programa de Pós-Graduação: Artes. 4 5 Agradecimentos Ao meu orientador, profº Dr. -
Society of Fellows News American Academy in Rome
SOCIETY OF FELLOWS NEWS AMERICAN ACADEMY IN ROME GARDENS SPRING 2004 From the Editor Catherine Seavitt FAAR’98 The Latin word hortus translates as and the delicacy of life itself, through Society of Fellows NEWS "kitchen garden", which certainly its very materiality. A field of golden SPRING 2004 implies a very different notion than wheat is certainly a powerful image - Published by the Society of Fellows of FAAR’98 that of a large public park or a private epitomized in Agnes Denes 's The American Academy in Rome pleasure garden. Conceptually, the Wheatfield, the planting and harvesting 7 East 60 Street kitchen garden embodies notions of of two acres of wheat at the Battery New York, NY 10022-1001 USA growth, careful tending, and suste- Park landfill, New York, in 1982. This tel 212 751 7200 www.sof-aarome.org Catherine Seavitt FAAR’98 nance, as well as a deeper notion of is a work that profoundly addresses Editor: Co-Editors: Stefanie Walker FAAR’01 text the stewardship of the land. The capitalism and hunger as well as the Joanne Spurza FAAR’89 news cycling of nature is visible in the sea- sustainability of our own humanity. Brian Curran FAAR’94 obits sonal passage of fruits and vegetables, Agnes' Wheatfield is particularly SOF Liason: Elsa Dessberg as is the quirky character of plants - poignant in light of the aftermath of the eternal return of the tomatoes September 11, 2001. Contents and the certain invasion of the A garden captures the spiritual SOF President’s Message 3 rhubarb. The challenges of a small notion of the eternal return, and per- From the AAR President, New York 4 kitchen garden certainly have some haps no city matches that spirit more From the AAR Director, Rome 6 News From Rome 8 analog with each of our own person- than Rome, the Eternal City. -
Changes in Cross-Section Geometry and Channel Volume in Two Reaches of the Kankakee River in Illinois, 1959-94
Changes in Cross-Section Geometry and Channel Volume in Two Reaches of the Kankakee River in Illinois, 1959-94 By PAUL J. TERRIO and JOHN E. NAZIMEK U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 96 4261 Prepared in cooperation with the KANKAKEE COUNTY SOIL AND WATER CONSERVATION DISTRICT Urbana, Illinois 1997 U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary U.S. GEOLOGICAL SURVEY Gordon P. Eaton, Director The use of firm, trade, and brand names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey. For additional information write to: Copies of this report can be purchased from: District Chief U.S. Geological Survey U.S. Geological Survey Branch of Information Services 221 N. Broadway Box 25286 Urbana, Illinois 61801 Denver, CO 80225 CONTENTS Abstract......................................................................................... 1 Introduction...................................................................................... 1 Purpose and Scope............................................................................ 3 Description of the Study Area................................................................... 4 Acknowledgments............................................................................ 4 Compilation and Measurement of Channel Cross-Section Geometry Data ..................................... 6 Momence Wetlands Reach ..................................................................... 6 Six-Mile Pool Reach ......................................................................... -
Momath's Intersection of Math And
Bridges 2020 Conference Proceedings Composite: MoMath’s Intersection of Math and Art Cindy Lawrence1 and Tim Nissen2 1Cindy Lawrence, National Museum of Mathematics, NYC; [email protected] 2Tim Nissen, National Museum of Mathematics, NYC; [email protected] Abstract That there are meaningful connections between art and mathematics is intuitively clear to mathematicians and mathematically-inspired visual artists, but the connection is often less clear to others, especially to those whose negative associations with mathematics during school-age years trigger emotions counter to feelings inspired by beautiful artworks. At the National Museum of Mathematics, the Composite gallery has been a laboratory of temporary art exhibitions. The introduction of tactile interactivity as a bridge between art and geometric forms in Solid Math, and the presentation of origami art through its often-overlooked mathematical makeup in Math Unfolded, highlighted these interconnections for visitors of all ages. New in Composite Since 2014, Composite, the gallery at the National Museum of Mathematics (MoMath) [2], has housed a series of temporary exhibitions of the work of mathematically-inclined artists including Antal Kelle ArtFormer, Miguel Berrocal, Matthew Brand, and Trevor and Ryan Oakes. In 2019, two exhibitions explored the connections between mathematics and art through multi-artist curated shows and physical interactives. Characteristic of the Museum proper, the collection of works and interactives encourages visitors to engage deeply with the content, integrating an array of models and artworks.. Solid Math, which ran from April through July of 2019, explored the geometry of regular polyhedra and showcased art based on these forms. Platonic, Archimedean, and Catalan polyhedra provided the formal constraints as well as the rhythmic underpinnings for the artists’ pieces presented in the show. -
Utah Museum of Fine Arts Evening for Educators February 21, 2007 • 5:30 Pm - 8:30 Pm Table of Contents
Book Arts Utah Museum of Fine Arts Evening for Educators February 21, 2007 • 5:30 pm - 8:30 pm Table of Contents Page Contents 2 List of Postcards 3 An African Folk Tale , Legge Written by Jacqueline Scuderi 4 lesson plan for An African Folk Tale Written by Louona Tanner 11 Ip, Serebrin & Anderton Written by Jacqueline Scuderi 12 lesson plan for Ip Written by Lola Beatlebrox 18 Fossil Ridge, Cotter Written by Jacqueline Scuderi 19 lesson plan for Fossil Ridge Written by Tiya Karaus 23 Celtic Portfolio Edition #11, Wilde Written by Jacqueline Scuderi 24 lesson plan for Celtic Portfolio Edition #11 Written by Jacqueline Scuderi 29 Labyrinths of the Mind, Book I, Bliss Written by Jacqueline Scuderi 31 lesson plan for Labyrinths of the Mind, Book I Written by Jacqueline Scuderi 33 Life Book: 1939-1976, Colby Written by Jacqueline Scuderi 34 lesson plan for Life Book: 1939-1976 Written by Tiya Karaus 37 Robert Sabuda: Paper Engineer Written by Robert Sabuda 39 lesson plan for Pop-up Book Written by Jennifer Jensen Evening for Educators is funded in part by the StateWide Art Partnership and The Richard K. and Shirley S. Hemingway Foundation 1 Book Arts Utah Museum of Fine Arts Evening for Educators February 21, 2007 • 5:30 pm - 8:30 pm List of Postcards 1. Willow Legge, British An African Folk Tale: Why the Sun and the Moon Live on the Sky, 1979 Serigraph and intaglio on paper Gift of Murray Herring Museum #1980.100A-J 2. Judith Serebrin with text by Nola Anderton, American Ip , 1990 Etching on paper Purchased with funds from Friends of the Art Museum Museum #1991.004.001 3. -
Bathsheba Grossman
gallery: bathsheba grossman “The universe is orderly and friendly and beautiful. Structure is this lovely, versatile thing.” “It’s either right or it’s wrong. It’s either elegant or not elegant. In math, those are actual properties. Everyone agrees.” 24 Based on mathematical structures, Bathsheba Grossman’s metal artworks are an example of digital sculpture given form. by Raven Hanna Bathsheba Grossman carries around her art wher- grasp. As you attempt to trace the labyrinthine for- ever she goes. She shows strangers her two- mations, you are drawn in, mesmerized. inch metal sculptures, the babies of her collection. Although her sculptures look mathematical, the People hold them, stare at them, love them, and quantitatively-challenged are not put off. “A lot buy them. In this way, she has sold on the spot to of people who don’t know anything about math or barmaids, secretaries, bus drivers, and mail deliverers. science buy these things,” she says. “There’s a The sculptures themselves are their own best lot of raw appeal. People approach them in different marketing. After selling a sculpture to Microsoft’s ways, but almost everybody sees that they are Mark Zbikowski, famous to computer geeks and of interest.” business buffs for developing MS-DOS software, Grossman grew up in a middle-class neighbor- she watched requests from other Microsoft employ- hood in Massachusetts with English professor ees roll in. Grossman makes art people want. parents. At Yale University, she shirked the family “I think they say something important about the tradition by pursuing a degree in mathematics. -
Galerije Antuna Augustin^I]A Original U Skulpturi
28–29 ANALI ANALI GALERIJE ANTUNA AUGUSTIN^I]A GOD. XXVIII–XXIX (2008.–2009.) • BR. 28–29 • STR. 1–472 • KLANJEC 2010. Simpozij ORIGINAL U SKULPTURI Klanjec, 4. – 6. lipnja 2008. ZBORNIK RADOVA 28 29 ISSN-0352-1826 UDK 71/77(058) ANALI GALERIJE ANTUNA AUGUSTIN^I]A GOD. XXVIII–XXIX (2008.–2009.) • BR. 28–29 • STR. 1–472 • Klanjec 2010. ISSN-0352-1826 UDK 71/77(058) CONTENTS SADR@AJ Editor’s Word Riječ urednika 5 5 LAVINIA BELUŠIĆ LAVINIA BELUŠIĆ The Concept of Originality in Pojam izvornosti u traktatima Rennaisance Italy Treatises (1435–1568) renesansne Italije (1435.–1568.) 35 9 IGOR FISKOVIĆ IGOR FISKOVIĆ The Case of the Renaissance Sculpture Slučaj renesansnog kipa Sv. Petra u of St. Peter in Vrboska Vrboskoj 51 37 VEDRANA GJUKIĆ-BENDER VEDRANA GJUKIĆ-BENDER Sculptor Innocenzo Spinazzi, Creator Innocenzo Spinazzi – kipar stvaratelj and Copyist i kopist 64 53 VESNA LOVRIĆ PLANTIĆ VESNA LOVRIĆ PLANTIĆ »The Montgolfier Brothers’ Balloon« »Balon braće Montgolfier« Luxurious Clock-Sculpture: Problems of Raskošan sat-skulptura: problemi Attribution and Dating atribucije i datacije 84 67 DR. JOSIP KOROŠEC JOSIP KOROŠEC The Role of Sculpture and the Uloga skulpture i značaj njezine Importance of Its Originality izvornosti 96 85 CONTENTS SADR@AJ MARTINA OŽANIĆ MARTINA OŽANIĆ Sculptural Group of The Holy Family – Skulpturalna grupa Svete Obitelji – Sharing Ideas and Authorship in pitanje udjela autorske invencije u Studies and Prints odnosu na grafički predložak 113 97 ANICA RIBIČIĆ-ŽUPANIĆ ANICA RIBIČIĆ-ŽUPANIĆ Francisco Pallas y Puig Francisco