Make your own free website on Tripod.com


 
3KbVISUAL MATHEMATICS

2Kb



 

 
Volume 1, No. 1, 1999

 
Volume 1, No. 2, 1999

 
Volume 1, No. 3, 1999

 
Volume 1, No. 4, 1999

 
Volume 2, No. 1, 2000

 
Volume 2, No. 2, 2000

 
Volume 2, No. 3, 2000

 
Volume 2, No. 4, 2000

 
Volume 3, No. 1, 2001

 
Volume 3, No. 2, 2001

Volume 3, No. 3, 2001

Volume 3, No. 4, 2001

Volume 4, No. 1, 2002

Volume 4, No. 2, 2002

Volume 4, No. 3, 2002

Volume 4, No. 4, 2002

Volume 5, No. 1, 2003

Volume 5, No. 2, 2003

Volume 5, No. 3, 2003

Volume 5, No. 4, 2003

Volume 6, No. 1, 2004

Volume 6, No. 2, 2004

Volume 6, No. 3, 2004

Volume 6, No. 4, 2004

Special E-book issue

Volume 7, No. 1, 2005

Volume 7, No. 2, 2005

Volume 7, No. 3, 2005

Volume 7, No. 4, 2005

Volume 8, No. 1, 2006

Volume 8, No. 2, 2006

Volume 8, No. 3, 2006

Volume 8, No. 4, 2006

Volume 9, No. 1, 2007

Volume 9, No. 2, 2007

Volume 9, No. 3, 2007

Volume 9, No. 4, 2007

Volume 10, No. 1, 2008

Volume 10, No. 2, 2008

Volume 10, No. 3, 2008

Volume 10, No. 4, 2008

Volume 11, No. 1, 2009

Volume 11, No. 2, 2009

Volume 11, No. 4, 2009

Volume 12, No. 1, 2010

Volume 12, No. 2, 2010

Volume 12, No. 3, 2010

Volume 12, No. 4, 2010

Volume 13, No. 1, 2011

Volume 13, No. 2, 2011

Volume 14, No. 1, 2012

Volume 14, No. 2, 2012

Volume 14, No. 3, 2012





 


 
Volume 1, No. 1, 1999 

 
 
 
1) Crowe, D.W.: PRECISE PERFECT COLORINGS OF ARCHIMEDEAN TESSELLATIONS

 
2) Dunham, D.: TRANSFORMATION OF HYPERBOLIC ESCHER PATTERNS

 
3) Gerdes, P.: ON LUNDA DESIGNS AND SOME OF THEIR SYMMETRIES

 
4) Hilton, P. and Pedersen, J.: SYMMETRY IN THEORY - 
MATHEMATICS AND AESTHETICS

 
5) Hilton, P. and Pedersen, J.: SYMMETRY IN PRACTICE - 
RECREATIONAL CONSTRUCTIONS

 
6) Hofman-Jablan, J.: TONALITY/ATONALITY - 
ORDER/DISORDER OR ORDER/NEW ORDER

 
7) Jablan, S.V.: ORDERING KNOTS

 
8) Kappraff, J.: SYSTEMS OF PROPORTION IN DESIGN AND
THEIR RELATIONSHIP TO DYNAMICAL SYSTEMS THEORY

 
9) Takaki, R.: RHEO-ART - APPLICATION OF FLUID DYNAMICS TO ART CREATION

 
10) Wegner, B.: TANGENTIAL SYMMETRIES OF PLANE AND SPACE CURVES

 
11) Weise, D.: PRINCIPLE OF MINIMAX AND RISE PHYLLOTAXIS 
(MECHANISTIC PHYLLOTAXIS MODEL)

 
12) Williams, K.: SYMMETRY IN ARCHITECTURE

 
 

PORTRAIT OF THE AUTHORS

This first issue of the journal became a "meeting place" of an international group of authors, representing five continents. Although the papers give reliable information about the authors, we add here some brief "informal" notes on all of them:

- Peter Hilton and Jean Pedersen (U.S.A.) are research mathematicians and university professors who also have a deep concern about mathematics teaching. They have collaborated extensively since 1980, producing over 100 joint papers and several books. One of their common interests is the discovery of interesting new areas of research arising from familiar mathematics at the secondary level - in the spirit of their great friend, the late George Pólya.

- Jadranka Hofman-Jablan (Yugoslavia) is a musicologist who published a monograph on symmetry in music (in Serbo-Croatian); she is the wife of the mathematician Slavik Jablan.

- Jay Kappraff (U.S.A.) is a mathematician who is the author of the book Connections, an important document of the "bridges" between art and science.

- John Langdon (U.S.A.) is a graphic artist whose book Wordplay: Ambigrams and Reflections on the Art of Ambigrams, with Martin Gardner's foreword, "reflects" (or "turns" into) a new genre at the border of art and mathematics.

- John Robinson (Australia) is sculptor who lives in Britain. Many of his works were commissioned by leading scientific institutions, and he also inspired, among others, a paper by H.S.M.Coxeter.

- Ryuji Takaki (Japan) is a physicist, the Editor of the journal Forma, the official publication of Katachi no kagaku kai (Society for Science on Form, Japan).

- Bernd Wegner (Germany) is a mathematician, the editor-in-chief of the oldest survey journal in the field of mathematics (Zentralblatt für Mathematik). His own research field is differential geometry.

- Dmitry Weise (Russia) is a medical doctor who also has time for the study of the Fibonacci numbers of the phyllotaxis (leaf arrangement).

- Kim Williams (U.S.A.) is a an architect who lives in Italy. She is the organizer of the international conferences Nexus: Relationships Between Architecture and Mathematics and also the editor of our sister electronic journal Nexus. Her new monograph Italian Pavements: Patterns in Space presents very exciting aspects of art and mathematics.
 




 
Volume 1, No. 2, 1999 

 
 
 
1) Avital, T.: FOOTPRINTS LITERACY:
THE ORIGINS OF ART AND PRELUDE TO SCIENCE

 
2) Avital, T.: MINDPRINTS: THE STRUCTURAL SHADOWS OF MIND-REALITY?

 
3) Goranson, H.T.: THE SOFT LOGICS OF THOMAS HARRIOT

 
4) Huff, W.S.: RESULTS OF FIVE STUDENTS FROM THE PROGRAMMED DESIGN ASSIGNMENT, IN THE FORMATIVE DESIGN STUDIO AT BUFFALO

 
5) Zenkin, A.A.: COGNITIVE VISUALIZATION OF THE CONTINUUM PROBLEM AND MIRROR SYMMETRIC PROOFS IN THE TRANSFINITE NUMBERS THEORY



 
SYMMETROGRAPHY PAPERS:

 
Nagy, D.: VISUAL MATHEMATICS: A MISSING LINK IN A SPLIT CULTURE

 
Nagy, D.: La Matemática Visual: Un eslabón perdido en una cultura dividida

 




 
Volume 1, No. 3, 1999 

 
 
 
1) Hilton, P. and Pedersen, J.: TWO REMARKABLE FAMILIES OF EQUILATERAL TRIANGLES WITHIN THE PASCAL HEXAGON - A TRIUMPH FOR SYMMETRY

 
2) Hilton, P. and Pedersen, J.: ON THE GEOMETRY AND COMBINATORICS 
OF THE ARRAY OF MULTINOMIAL COEFFICIENTS

 
3) Leyton, M.: GROUP THEORY AND ARCHITECTURE 1: NESTED SYMMETRIES

 
4) Spinadel, V.W. de: THE FAMILY OF METALLIC MEANS

 
5) Sullivan, J.M.: THE "OPTIVERSE" AND OTHER SPHERE EVERSIONS



 
STUDENT PAPERS:

 
Kozomara, A.: DISCRETE PLANE SYMMETRY GROUPS



 



 
Volume 1, No. 4, 1999 

 
 
 
1) Barrallo, J. and Jones D.M.: COLORING ALGORITHMS 
FOR DYNAMICAL SYSTEMS IN THE COMPLEX PLANE

 
2) Kocic Lj.M.: PORTRAITS OF NUMBERS

 
3) Leyton M.: GROUP THEORY AND ARCHITECTURE, 2:
WHY SYMMETRY/ASYMMETRY?

 
4) Ogawa T.: AN ESSENTIALLY-THREE-DIMENSIONAL QUASICRYSTAL 

 
5) Ogawa T.: SYMMETRY OF THREE-DIMENSIONAL QUASICRYSTALS

 
6) Ogawa T. and Collins R.: CHAINS, FLOWERS, RINGS AND PEANUTS:
GRAPHICAL GEODESIC LINES AND THEIR APPLICATION TO PENROSE TILING



 
SYMMETROGRAPHY PAPERS:

 
Nagy, D.: SYMMETRO-GRAPHY (BIBLIOGRAPHIC SECTION) 


2000



 
Volume 2, No. 1, 2000 

 
 
 
1) Ogawa, T.: PROBLEMS IN A DIGITAL DESCRIPTION OF A CONFIGURATION OF ATOMS AND SOME OTHER GEOMETRICAL TOPICS IN PHYSICS 

 
2) Ogawa, T. and Nakajima, Y.: FRUSTRATION, DEGENERACY AND FORMS 

 
3) Perez-Gomez, R. and Ruiz, C.: CHROMATIC PLANE COMPOSITIONS

 
4) Perez-Gomez, R. and Ruiz, C.: METHODS OF PERFECT COLORING

 
5) Sarhangi, R. and Martin, B.D.: THE CIRCLE: PARADOX AND PARADIGM

 
6) Yevin, I.: AMBIGUITY AND ART



 
EDUCATIONAL PAPERS:

 
Dreifus, T. and Eisenberg, T.: ON SYMMETRY IN SCHOOL MATHEMATICS 

 
Lipkovski A.T.: VISUALIZATION OF SIMPLE ALGEBRO-GEOMETRIC IDEAS



 



 
Volume 2, No. 2, 2000 

 
 
 
1) Kocic, Lj. and Simonicelli, A.C.: FRACTAL INTERPOLATION IN
CREATING PREFRACTAL IMAGES

 
2) Lungu, A.: THE RECENT GENERALIZATIONS
OF COLORED SYMMETRY

 
3) Meilan, P.F., Creus, M. and Garavaglia, M.: GENERATION OF 
QUASI-MOIRÉ PATTERNS: FRACTALITY AND PERCOLATION

 
4) Ogawa, T. and Watanabe, Yo.: GRAPHICAL GEODESIC LINES
APPLIED FOR SOME QUASIPERIODIC TILING 



 



 
Volume 2, No. 3, 2000 
"BRIDGES 2000" in "VisMath"

 
 
 
1) Field M.: THE ART AND SCIENCE OF SYMMETRIC DESIGN 

 
2) Gailiunas P.: SPIRAL TILINGS

 
3) Hart G.: THE MILLENNIUM BOOKBALL

 
4) Kaplan C.: COMPUTER GENERATED ISLAMIC STAR PATTERNS

 
5) Kappraff J. and Adamson W.: A FRESH LOOK AT NUMBER

 
6) Sarhangi R.: PERSIAN ARTS: A BRIEF STUDY

 
7) Sequin C.: "-TO BUILD A TWISTED BRIDGE-"

 

This issue of the journal is dedicated to the "BRIDGES: Mathematical Connections in Art, Music, and Science" Conference (Southwestern College, Winfield, KS, July 28 - 30, 2000) organized by Reza Sarhangi. The first six papers are republished in the electronical form from the Conference Proceedings (ISBN-0-9665201-2-2), with the kind permition of Reza Sarhangi, the Editor of the Proceedings. 



 



 


 
Volume 2, No. 4, 2000 

 
 
 
1) Van Dyke, J.R.: OPTIMAL SPHERICAL PACKING 
OF CIRCLES AND HILBERT'S 14TH PROBLEM 

 
2) Jablan, S.V.: ARE BORROMEAN LINKS SO RARE?

 
3) Ling Ngo, D.C. and Lian Seng, T.: A MATHEMATICAL 
THEORY OF INTERFACE AESTHETICS


2001




 
Volume 3, No. 1, 2001 
"BRIDGES 1998, 1999" in "VisMath"

 
 
 
1) Friedman N.: HYPERSEEING, HYPERSCULPTURES AND SPACE CURVES 

 
2) Golubitsky M.and Melbourne I.: A SYMMETRY CLASSIFICATION OF COLUMNS

 
3) Lubachevsky B.D., Graham R.L. and Stillinger F.H.: SPONTANEOUS PATTERNS IN DISK PACKINGS

 
4) Martin B.D. and Sarhangi R.: SYMMETRY, CHEMISTRY AND ESCHER'S TILES

 
5) Peden D.D.: BRIDGES OF MATHEMATICS, ART, AND PHYSICS

 
6) Sequin C.: ANALOGIES FROM 2D TO 3D EXERCISES IN DISCIPLINED CREATIVITY



 
EDUCATIONAL PAPERS:

 
Kaladzievski S.: INTEGRATION BY PARTS: A VISUAL PROOF




 
Volume 3, No. 2, 2001 
"BRIDGES 1998, 1999, 2000, 2001" in "VisMath"

 
 
 
 
1) Barrallo J.: FRACTALS AND MULTI LAYER COLORING ALGORITHMS

 
 
2) Bulatov V.: AN INTERACTIVE CREATION OF POLYHEDRA STELLATIONS WITH VARIOUS SYMMETRIES

 
 
3) COREY CEROVSEK: A WORLD CLASS VIOLINIST AND MATHEMATICIAN

 
 
4) Collins B.: GEOMETRIES OF CURVATURE AND THEIR AESTHETICS

 
 
5) Crowe D.W.: SYMMETRIES OF CULTURE

 
 
6) Daniel D.F., Jablan S., Schmidt D.: QUILTED SYMMETRY

 
 
7) Fathauer R.W.: SOME COMMON THEMES IN VISUAL MATHEMATICAL ART

 
 
8) Friedman N.: KNOTS AND MULTIPLE MÖBIUS BAND MINIMAL SURFACES

 
 
9) Jablan S.: MIRROR CURVES

 
 
10) Krawczyk R.J.: MORE CURVED SPIROLATERALS

 
 
11) Perry C.O.: CONTINUUM, BROKEN SYMMETRY, AND MORE

 
 
12) POETRY OF GAR BETHEL

 
 
13) Radovic Lj. and Jablan S.: ANTISYMMETRY AND MODULARITY IN ORNAMENTAL ART

 
 
14) Rousseau I.: SPECTRAL LIGHT AS STRUCTRED SPACE

 
 
15) Sims J.: TIMESCULPTURE

 

This issue of the journal is dedicated to the "BRIDGES: Mathematical Connections in Art, Music, and Science" Conference (Southwestern College, Winfield, KS, July 1989, 1990) organized by Reza Sarhangi. The papers are republished in the electronical form from the Conference Proceedings (ISBN-0-9665201-0-6, ISBN-0-9665201-1-4, ISBN-0-9665201-2-2), with the kind permition of Reza Sarhangi, the Editor of the Proceedings. 



 



 

Volume 3, No. 3, 2001 

 
 
SPECIAL ISSUE: INTERSECTIONS OF ART AND SCIENCE





Volume 3, No. 4, 2001 

 
1) Friedman N.: HYPERSEEING, HYPERSCULPTURES, KNOTS, AND MINIMAL SURFACES

 
2) Korren A.: IDENTICAL DUAL LATTICES AND SUBDIVISION OF SPACE

 
3) Morrison T.: THE GEOMETRY OF HISTORY; 032147658

 
4) Wichmann B. and Dawes J.: A NEW CLASS OF TILINGS WITH TWO PROTOTILES


2002



Volume 4, No. 1, 2002 

 
1) Crass S.: POLYNOMIALS, SYMMETRY, AND DYNAMICS:
AN UNDERTAKING IN AESTHETICS

 
2) Gerdes P.: FROM LIKI-DESIGNS TO CYCLE MATRICES:
THE DISCOVERY OF ATTRACTIVE NEW SYMMETRIES

 
3) Gerdes P.: m-CANNONIC MIRROR CURVES

 
4) Hafner I., Zitko T. and Jurcic-Zlobec B.: GALLERY OF RHOMBIC POLYHEDRA

 
5) Ippoliti E.: COGNITIVE VISUALIZATION OF SOME
INTEGER - VALUED POLYNOMIALS

 
6) Kobes R. and Letkeman H.: NON-LINEAR FRACTAL INTERPOLATING FUNCTIONS

 
7) Stewart B.D.: NEWTON, CHEBYSSVEV, AND HALLEY BASINS
OF ATTRACTION; A COMPLETE GEOMETRIC APPROACH

 
8) Palistrant A.F.: PROFESSOR A. M. ZAMORZAEV (1927-1997)
AND KISHINEV SCHOOL OF DISCRETE GEOMETRY

 
 
PAPERS FROM ViVeMath

 
9) Endl K.: SOFTWARE FOR GEOMETRY

 
10) Jablan S.: MODULARITY IN SCIENCE AND ART

 
10) Jablan S.: MODULARIDAD EN EL ARTE

 
11) Kocic Lj. M.: ART ELEMENTS IN FRACTAL CONSTRUCTIONS

 
12) Knezevic I., Sazdanovic R. and Vukmirovic S.:
VISUALIZATION OF THE LOBACHEVSKIAN PLANE

 
13) Lipkovski A.: THE EDUCATIONAL USE OF
MATHEMATICAL SOFTWARE: TECHNIQUES AND EXAMPLES

 
14) Malkowsky E. and Velickovic V.: A SOFTWARE FOR THE VISUALIZATION OF DIFFERENTIAL GEOMETRY

 
15) Markovich S.:
AMODAL COMPLETION IN VISUAL PERCEPTION

 
16) Radovic Lj.: RECONSTRUCTION OF ORNAMENTS

 
17) Stefanovska Lj., Grcev T. and Gegovska-Zajkova S.:
VISUALIZATION OF THE REACTION ZONE SPREADING FOR
AN ALUMOTHERMIC (REDOX) REACTION

 
18) Stefanovska Lj., Andonovic B. and Gegovska-Zajkova S.:
OF AN ITERATIVE PROCEDURE FOR SOLVING THE
OPTIMIZATION PROBLEM INTO AN ELLIPSOID





Volume 4, No. 2, 2002 

 
1) Gerdes P.: CYLINDER MATRICES

 
2) Gerdes P.: HELIX MATRICES

 
3) Hafner I. and Zitko T.: INTRODUCTION TO GOLDEN RHOMBIC POLYHEDRA

 
4) Hafner I. and Zitko T.: RELATIONS AMONG RHOMBIC, PLATONIC AND ARCHIMEDEAN SOLIDS

 
5) Hafner I. and Zitko T.: FROM DISSECTION OF THE CUBE TO SPACE FILLING WITH PROLATE RHOMBOEDRA ND RHOMBIC DODECAHEDRA OF THE SECOND KIND





Volume 4, No. 3, 2002 

 
1) Cerf C.: A FAMILY OF IMPOSSIBLE FIGURES
STUDIED BY KNOT THEORY

 
2) Gerdes P.: A NOTE ON CHESSBOARD MATRICES

 
3) Gerdes P.: TWILL-PLAITED OCTAGONAL DESIGNS

 
4) Giunti R.: ANALYSING "CHESS"

 
5) Hafner I. and Zitko T.: TWO CONVEX POLYHEDRA WITH A COMMON NET

 
6) Huff W.S.: ADDITIONAL RESULTS FROM THE PROGRAMMED DESIGN
ASSIGNMENT, IN THE FORMATIVE DESIGN STUDIO AT BUFFALO

 
7) Rojas C.C.: GEOMETRY OF THE PARABOLA ACCORDING TO THE GOLDEN NUMBER






Volume 4, No. 4, 2002 

 
1) Maynard P.M.: ISOHEDRALLY COMPATIBLE TILINGS

 
2) Schulze-Fielitz E.: METAEDER

 
3) Sigaud N.: ANACOM PROJECT

 
4) Tennant R.F.: SUBGROUP LATTICES FOR CRYSTALLOGRAPHIC GROUPS


EDUCATIONAL PAPERS:

 
Tennant R.F.: INTERDISCIPLINARY TEACHING STRATEGIES
IN THE WORLD OF HUMANISTIC MATHEMATICS

 
 



2003



Volume 5, No. 1, 2003 

 
1) Gerdes P.: PLAITED STRIP PATTERNS ON TONGA HANDBAGS
IN INHAMBANE (MOZAMBIQUE) – AN UPDATE

 
2) Hafner I. and Zitko T.: COLOURING PLATONIC SOLIDS

 
3) Kappraff J. and Adamson G.W.: A UNIFIED THEORY OF PROPORTION

 
4) Lucca G.: REPRESENTING SEASHELLS SURFACE

 
5) Weise D.: THE PYTHAGOREAN APPROACH TO PROBLEMS OF
PERIODICITY IN CHEMISTRY AND NUCLEAR PHYSICS

 
6) Wertheim I. and Movshovitz-Hadar N.: VISUALIZATION VS. VERBALIZATION

 




Volume 5, No. 2, 2003 

 
1) Gerdes P.: DIVIDING THE SIDES OF A TRIANGLE
IN PROPORTIONAL PARTS

 
2) Hafner I. and Zitko T.: ON CERTAIN CONSTRUCTION OF
RHOMBIC HEXACONTAHEDRA


SOFTWARE:

 
Ochiai M., Imafuji N., Jablan S. and Sazdanovic R.:
KNOT THEORY PROGRAMS KNOT2000 (K2K) + LinKnot (K2KC)

 




 

Volume 5, No. 3, 2003 

 
1) Hafner I. and Zitko T.: FOUR PROBLEMS ON DODECAHEDRON

 
2) Hafner I. and Zitko T.: MAZES ON SURFACES

 
3) Hafner I. and Zitko T.: PROJECTIONS OF THE WORLD
ONTO CONVEX POLYHEDRA

 
4) Hafner I. and Zitko T.: TWO BASIC PROBLEMS OF POLYHEDRA NETS

 
5) Lucca G.: DECORATIONS BY MEANS OF GENERALIZED CLOTHOIDS

 



Volume 5, No. 4, 2003 

 
1) Barry P.: THE FOURIER ANALYSIS OF BEZIER CURVES

 
2) Gerdes P.: OBLIQUE ALTITUDES AND BISECTORS

 
3) Hoffman W.C.: SYMMETRY IN PSYCHOLOGY

 
 



2004



 

Volume 6, No. 1, 2004 

 
1) Lucca G.: MODELLING STARFISHES SURFACE

 
2) Puente C.E. and Puente M.G.: ICE CRYSTALS INSIDE THE BELL

 
3) Zamorzaeva E.: ENUMERATION OF 2-ISOHEDRAL TILINGS ON THE SPHERE

 



Volume 6, No. 2, 2004 

 
1) Chun-Wang Sun and Guan-Ze Liao: AN AESTHETIC EXPLORATION OF RELATIVE MOTIONS


EDUCATIONAL PAPERS:

Gompa R.R. and Gompa V.L.: ESTIMATING MATHEMATICAL INFORMATION ON GRAPHS: A SCIENTIFIC APPROACH  


Volume 6, No. 3, 2004 

 
1) Baker J. and King D.: THE USE OF VISUAL SCHEMA TO FIND PROPERTIES OF A HEXAGON

 
2) Lucca G.: SYMMETRICAL PATTERNS BY MEANS OF CONTOUR PLOTS


Volume 6, No. 4, 2004 

 
1) Bleeicher L.S.: SERIAL POLAR TRANSFORMATIONS OF SIMPLE GEOMETRIES

 
2) Djellit I. and Boukemara I.: BIFURCATIONS AND ATRACTORS IN BOGDANOV MAP

 
3) Pais J. and Singer R.: VISUAL MAGIC SQUARES AND GROUP ORBITS I

 
4) Pennock S.: OF TORUS AND TURK'S-HEAD KNOTS: A POLAR TRIGONOMETRIC MODELING

 
5) Zalaya R. and Barrallo J.: CLASSIFICATION OF MATHEMATICAL SCULPTURE



 


Special E-book issue  

 
Gerdes P.: BASKETRY, GEOMETRY AND SYMMETRY IN AFRICA AND AMERICAS

 
 



2005




Volume 7, No. 1, 2005 

 

"BRIDGES 2004" in "VisMath"

 
 
1) Akleman E., Edmundson P. and Ozener O.: A GENERALIZED VERTEX TRUNCATION SCHEME
TO CONSTRUCT INTRIGUING POLYHEDRAL SCHEME

 
2) Bier C. and Masunaga D.K.: ISLAMIC ART AT DORIS DUKE'S SHANGRI LA-
PLAYING WITH FORM AND PATTERN

 
3) Fisher G. and Mellor B.: TOPOLOGY OF CELTIC KNOT DESIGNS

 
4) Gilley A.: FRACTALLED: THE INTERSTITIAL SPACES AND FRANK GEHRY

 
5) Hansen-Smith B.: FOLDING THE CIRCLE AS BOTH WHOLE AND PART

 
6) Hart G.: A SALAMANDER SCULPTURE BARN RAISING

 
7) Kappraff J.: ANATOMY OF A BUD

 
8) Roelofs R.: GLIDE REFLECTION AND OTHER COMBINED TRANSFORMATIONS

 
9) Sarhangi R., Jablan S. and Sazdanovic R.: MODULARITY IN MEDIEVAL PERSIAN MOSAICS:
TEXTUAL, EMPIRICAL, ANALYTICAL, AND THEORETICAL CONSIDERATIONS

 
10) Smith J., Akleman E., Davison R. and Keyser J.: MULTICAM: A SYSTEM FOR INTERACTIVE
RENDERING OF ABSTRACT DIGITAL IMAGES

 

The special Issue of "Visual Mathematics" dedicated to the Conference "Bridges 2004" includes only those articles that (a) were presented during the Conference, (b) their electronic versions were available, and (c) their subjects are related to the "Visual Mathematics" general theme.
 


Volume 7, No. 2, 2005 

 
1) Korren A.: 2-MANIFOLD SURFACES AND SPACE PARTITIONS

 
2) Palmer C.: SPIRAL TILINGS WITH S-CURVES AND C-CURVES
USING COMBINATIONS TO AUGMENT TRADITION

 
3) Schlatter M.: HOW TO CREATE MONOLINEAR MIRROR CURVES

 


Volume 7, No. 3, 2005 

 
SYMMETRY: ART AND SCIENCE
Sixth Interdisciplinary Symmetry Congress and Exhibition, Tihany, Hungary, October 22-29, 2004

 


Volume 7, No. 4, 2005 

 
1) Liao G. and Sun C.:GEOMETRIC PATTERN DESIGN WITH
RECURSIVE PURSUIT RELATIVE MOTIONS

 
2) Pennock S.: TURK's HEAD KNOTS (BRAIDED BAND KNOTS)
- A MATHEMATICAL MODELING

 
 



2006




Volume 8, No. 1, 2006 

 

"BRIDGES 2005" in "VisMath"

 
 
1) Burns A.M.: RECURSION IN NATURE, MATHEMATICS AND ART

 
2) Crowe D.W. and Washburn D.C.: GEOMETRICAL, PERCEPTUAL AND CULTURAL PERSPECTIVES ON
FIGURE/GROUND DIFFERENCES IN BAKUBA PATTERN

 
3) Dawson R.J.MacG.: SOME NEW TILINGS ON THE SPHERE
WITH CONGRUENT TRIANGLES

 
4) Hart G.W.: ORDERLY TANGLES REVISITED

 
5) Kalantari B.: TWO AND THREE-DIMENSIONAL ART
INSPIRED BY POLYNOMIOGRAPHY

 
6) Krawczyk R.J.: FERMAT'S SPIRAL MANDALAS

 
7) Roelofs R.: THREE-DIMENSIONAL AND DYNAMIC CONSTRUCTIONS
BASED ON LEONARDO GRIDS

 

The special Issue of "Visual Mathematics" dedicated to the Conference "Bridges 2005" includes only those articles that (a) were presented during the Conference, (b) their electronic versions were available, and (c) their subjects are related to the "Visual Mathematics" general theme.
 


Volume 8, No. 2, 2006 

 
1) Gerdes P.: SYMMETRIES OF ALTERNATING CYCLE MATRICES

 
2) Gerdes P.: ON THE REPRESENTATION AND MULTIPLICATION OF
BASIC ALTERNATING CYCLE MATRICES

 
3)Rigby J. and Wichmann B.: SOME PATTERNS USING SPECIFIC TILES



 
EDUCATIONAL PAPERS:

 
Miyadera R. and Minematsu D.: A BEAUTIFUL FIGURE MADE OF 99999..9n

 


Volume 8, No. 3, 2006 

 
1) Hafner I. and Zitko T.: A DISSECTION OF TWO RHOMBIC DODECAHEDRA
OF THE SECOND KIND TO A CUBE

 
2) Hafner I. and Zitko T.: A DISSECTION OF QUARTER OF RHOMBIC
DODECAHEDRON OF THE SECOND KIND TO A CUBE

 
3) Hafner I. and Zitko T.: A DISSECTION OF RHOMBIC TRIACONTAHEDRON

 
4) Stakhov A.and Rozin B.: THE GOLDEN SECTION, FIBONACCI SERIES AND
NEW HYPERBOLIC MODELS OF NATURE

 


Volume 8, No. 4, 2006 

 
1) Friedman N.: EVA HILD: TOPOLOGICAL SCULPTURE FROM LIFE EXPERIENCE

 
2) Hess M.C.: BINARY SYMMETRY

 
3) Hafner I. and Zitko T.: DISSECTION OF RHOMBIC 36-HEDRON
TO A TETRAHEDRON AND A TRUNCATED TETRAHEDRON

 
4) Hafner I. and Zitko T.: EQUIDECOMPOSITION OF RHOMBOHEDRON,
HEXAGONAL PRISM, AND RHOMBIC DODECAHEDRON

 
5) Hafner I. and Zitko T.: HINGED DISSECTION OF A HALF OF RHOMBIC ICOSAHEDRON

 
6) Hafner I. and Zitko T.: HINGED DISSECTION OF A RHOMBIC SOLID
TO THE TRUNCATED OCTAHEDRON

 
7) Hafner I. and Zitko T.: HINGED DISSECTION OF A RHOMBIC SOLID
TO THE TRUNCATED CUBOCTAHEDRON

 
8) Hafner I. and Zitko T.: INTRODUCTION TO RHOMBIC POLYHEDRA

 
9) Kappraff J.: COMPLEXITY AND CHAOS THEORY IN ART

 
 



2007




Volume 9, No. 1, 2007 

 
1) Hafner I.: LIVE 3D ANIMATIONS TO SOLUTION OF
CONWAY-RADIN-SADUN PROBLEM

 
2) Hafner I.: ANIMATED PROOF OF
CONWAY-RADIN-SADUN PROBLEM

 
3) Hafner I. and Zitko T.: DISSECTION OF CONCAVE TRIACONTAHEDRON

 
4) Miyadera R. et all.: PASCAL LIKE TRIANGLES AND SIERPINSKI LIKE GASKETS


 

 


 
webMathematica BOOK:

 
Jablan S. and Sazdanovic R.: LINKNOT
 

 
 




 

Volume 9, No. 2, 2007 

 
1) Hafner I.: HINGED DISSECTION OF A "RHOMBIC" SOLID TO THE TRUNCATED ICOSIDODECAHEDRON

 
2) Hafner I.: DISSECTION OF A RHOMBIC SOLID TO THE TRUNCATED DODECAHEDRON AND THE ICOSAHEDRON

 
3) Hafner I.: EQUIDECOMPOSABILITY OF PENTAGONAL ANTIPRISM AND METABIDIMINISHED ICOSAHEDRON

 
4) Hafner I.: DISSECTION OF TRIANGULAR HEBESPHENOROTUNDA, STEWART TOROID, AND DRILLED PENTAGONAL GYROBICUPOLA

 
5) Hafner I.: PAPER MODEL SOLUTION OF CONWAY-RADIN-SADUN PROBLEM

 
6) Hafner I.: DECOMPOSITION OF THREE BILUNABIROTUNDAS AND DODECAHEDRON TO RHOMBIC SOLIDS

 
7) Hafner I.: DISSECTION OF TRIDIMINISHED ICOSAHEDRON (J63) AND STEWART TOROID G3 TO
RHOMBIC SOLIDS, AND DISSECTION OF ICOSAHEDRON AND DRILLED G3 TO RHOMBIC SOLIDS

 
8) Hafner I.: DISSECTION OF SMALL STELLATED DODECAHEDRON AND GREAT STELLATED
DODECAHEDRON TO RHOMBIC TRIACONTAHEDRON AND HEXACONTAHEDRON

 
9) Marar T.: PROJECTIVE PLANES AND THE TRIPARTITE UNITY

 
10) Wichmann B. and Rigby. J.: A PENROSE-TYPE ISLAMIC INTERLACING PATTERN

 



 

e-BOOK:

 
Hofman-Jablan J.: SYMMETRY OF MUSICAL WORK

 

Volume 9, No. 3, 2007 

 
1) Gerdes P.: MWANI COLOUR INVERSION, SYMMETERY AND CYCLE MATRICES

 
2) Hafner I.: 4-PIECE DISSECTION OF JUEL'S PYRAMID TO A TRIANGULAR PRISM

 
3) Hafner I.: VISUAL EXAMPLES OF A THEOREM OF AXONOMETRY

 
4) Hafner I.: THREE DIMENSIONAL ILLUSTRATIONS FOR SOME PROPOSITIONS FROM EUCLID'S ELEMENTS

 
5) Hafner I.: 3D ILLUSTRATIONS TO CHAPTER 8 OF CROMWELL'S POLYHEDRA

 
6) Stakhov A.: THREE "KEY" PROBLEMS OF MATHEMATICS ON THE STAGE OF ITS ORIGIN,
THE "HARMONY MATHEMATICS" AND ITS APPLICATIONS IN CONTEMPORARY MATHEMATICS,
THEORETHICAL PHYSICS AND COMPUTER SCIENCE

 
7) Zefiro L.: REVIEW OF ALTERNATIVE CHOICES CONCERNING FACE COLOURING OF ALL
THE REGULAR CONVEX POLYHEDRA AND A PAIR OF CATALAN POLYHEDRA, THE RHOMBIC
DODECAHEDRON AND THE RHOMBIC TRIACONTAHEDRON

 



Volume 9, No. 4, 2007 

 
1) SYMMETRY: ART AND SCIENCE
Book of Extended Abstracts of the 7th Interdisciplinary Congress
and Exhibition of ISIS-Symmetry and the
6th National and 3rd International Congress of SEMA
FORM AND SYMMETRY, Buenos Aires, Argentina, 2007

 
2) Burt M.: PERIODIC SPONGE SURFACES AND UNIFORM SPONGE
POLYHEDRA IN NATURE AND IN THE REALM OF THE THEORETICALLY IMAGINABLE

 
3) Olguin G., Castellano L, Andrade E., Abraham M., and y de la Fuente, F.: PAS DE DEUX

 
4) Klein P.: "INTERMEDIATE MATTER": CONJECTURES ON IMPONDEROUS MATTER
AS INDUCED BY KEY CONCEPTS OF SYMMETRY

 
5) Zefiro L. and Ardigň M.R.: DESCRIPTION OF THE FORMS BELONGING TO THE 235 AND m35
ICOSAHEDRAL POINT GROUPS STARTING FROM THE PAIRS OF DUAL POLYHEDRA:
ICOSAHEDRON-DODECAHEDRON AND ARCHIMEDEAN POLYHEDRA-CATALAN POLYHEDRA

 
 



2008




Volume 10, No. 1, 2008 

 
1) Funes G., Garavaglia L. and Garavaglia M.: HIDDEN SYMMETRIES AMONG PRIMES

 
2) Hafner I.: DISSECTIONS OF GOLDEN RHOMBOEDRA

 
3) Hafner I.: GERLING'S DISSECTION



Volume 10, No. 2, 2008 

 
1) Meel D. and Youse (Gyrko) D.: NO-SEW MATHEMATICAL QUILTS:
NEEDLING STUDENTS TO EXPLORE HIGHER MATHEMATICS

 
2) Stakhov A.: THE "STRATEGIC MISTAKES" IN THE MATHEMATICS DEVELOPMENT
AND THE ROLE OF THE HARMONY MATHEMATICS FOR THEIR OVERCOMING

 
3) Takaki R.: INTERACTION OF SCIENCE AND ART THROUGH EDUCATIONAL SYSTEM



Volume 10, No. 3, 2008 

 
1) Abaza H.: NEW APPROACH FOR UNDERSTANDING THE GOLDEN SECTION

 
2) Burt M.: UNIFORM NETWORKS IN 3-DIMENSIONAL SPACE

 
3) Galiunas P.: SOME MONOHEDRAL TILINGS DERIVED FROM REGULAR POLYGONS

 
4) Ivancevic T., Ivancevic N. and Jovanovic S.: SCIENCE AND ART IN REPRESENTING THE FIFTH DIMENSION

 
5) Keiter J.P.: THE PROJECTION SPHERE

 
6) Zefiro L.: GENERATION OF AN ICOSAHEDRON BY THE INTERSECTION OF FIVE TETRAHEDRA:
GEOMETRICAL AND CRYSTALLOGRAPHIC FEATURES OF THE INTERMEDIATE POLYHEDRA



Volume 10, No. 4, 2008 

 
1) Perez J-C.: SYMMETRY AND ASYMMETRY IN MENDELEIEV'S PERIODIC TABLE PREDICTIVE EQUATION

 
2) Redondo Buitrago A. and Reyes Iglesias E.: THE GEOMETRY OF THE CORDOVAN POLYGONS

 
 



2009




Volume 11, No. 1, 2009 

 
1) Stakhov A.: DIRAC'S PRINCIPLE OF MATHEMATICAL BEAUTY, MATHEMATICS
OF HARMONY AND "GOLDEN" SCIENTIFIC REVOLUTION

 
2) Zefiro L. and Ardigo' M.R.: WHAT BECOME OF THE CONTROVERSAL FORTEENTH ARCHIMEDEAN SOLID,
THE PSEUDO RHOMB-CUBOCTAHEDRON?


Volume 11, No. 2, 2009 

 
1) Naito M., Doro S., Minematsu D., and Miyadera R.: THE SELF-SIMILARITY OF THE JOSEPHUS PROBLEM AND ITS VARIANTS

 
2) Taylor L.: DECORATIVE KNOTTING USING TRIGONOMETRIC PARAMETRIZATIONS

 
3) Zefiro L. and Ardigo' M.R.: PLATONIC AND CATALAN POLYHEDRA AS ARCHETYPES OF FORMS
BELONGING TO THE CUBIC AND ICOSAHEDRAL SYSTEMS


Volume 11, No. 3, 2009 

 
1) Astrom A., Astrom C.: OCTAGONAL KNOTWORKS: A MATHEMATICAL APPROACH

 
2) Naito M., Yamauchi T., Matsui H., Inoue T., Tomari Y., Nashimura K., Nakaoka T., Minematsu D., Miyadera R.:
COMBINATORIAL GAMES AND BEAUTIFUL FRAPHS PRODUCED BY THEM

 
3) Zefiro L.: DISSECTION OF THE RHOMB-ICOSIDODECAHEDRON IN ELEMENTARY REGULAR-FACED
POLYHEDRA AND SUBSEQUENT REASSEMBLY LEADING TO A SET OF JOHNSON'S POLYHEDRA

 
4) Zefiro L.: COLLECTION OF FORMS RESULTING FROM ALL THE COMBINATIONS
OF THE PLATONIC AND CATALAN POLYHEDRA WHICH CHARACTERIZE THE m3 5 ICOSAHEDRAL POINT GROUP


Volume 11, No. 4, 2009 

 
1) Miyadera R., Minematsu D., Inoue T., Nakaoka T., Nashimura K., Naito M., Tomari Y., Yamauchi T., Totani, N.:
CURIOUS PROPERTIES OF REITERATED PROCESSES AND BEAUTIFUL GRAPHS MADE BY THEM

 
2) Zefiro L.: COLLECTION OF THE COUPLES OF THE ARCHETYPAL COMPOUND FORMS WHICH ARE DIFFERENT
IN THE 235 AND m3 5 ICOSAHERDAL POINT GROUPS

 
 



2010




Volume 12, No. 1, 2010 


Special E-book issue dedicated to E. Lendvai  

 
Lendvai E.: SYMMETRIES OF MUSIC

 
Lendvai E.: SYMMETRIEN IN DER MUSIK

 
EXCERPTS OF LENDVAI'S WORKS



Volume 12, No. 2, 2010 

 
1) Gerdes P.: PERMUTATIONS AND COPI MATS, CHIDENGUELE, MOZAMBIQUE

 
2) Gerdes P.: A WAY TO INTERLACE AN OCTAGONAL PRISM INVENTED
BY A COPI BASKET MAKER IN SOUTHEAST MOZAMBIQUE


Conjectures  

 
1) Labarque P.: BLUEPRINT FOR A CLASSIC PROOF OF THE 4 COLOR THEOREM


E-book by Naomi Asakura  

 
Asakura N.: FUNDAMENTAL PROBLEMS OF CREATING IN TWO-DIMENSIONAL SPACE



Volume 12, No. 3, 2010 

 
1) Harries J.G.: SHAPE ANALYSIS, VISUAL ART AND THE AXIS OF SYMMETRY

 
2) Naito M., Yamauchi T., Minematsu D. and Miyadera R.: THE JOSEPHUS PROBLEM IN BOTH DIRECTIONS

 
3) Petrovic M. and Obradovic M.: FORMING A REGULAR PENTAGON, DECAGON AND PENTAGRAM USING ORIGAMI TECHNIQUE

 
4) Zefiro L.: THE COMPOUND OF THREE OCTAHEDRA AND A REMARKABLE COMPOUND OF
THREE SQUARE DIPYRAMIDS, THE ESCHER'S SOLID


Volume 12, No. 4, 2010 

 
1) Bodnar O.: DYNAMIC SYMMETRY IN NATURE AND ARCHITECTURE

 
 



2011




Volume 13, No. 1, 2011 

 
1) Blanco M.F.B. and de Camargo Harris A.L.N.: SYMMETRY GROUPS IN THE ALHAMBRA

 
2) Carter J.S. and Mullens D.: HERON'S FORMULA FROM A 4-DIMENSIONAL PERSPECTIVE

 
3) Taylor L.D.: DECORATIVE KNOT PATTERNS



Volume 13, No. 2, 2011 

 
1) Bodnar O.: GEOMETRIC INTERPRETATION AND GENERALIZATION
OF THE NONCLASSICAL HYPERBOLIC FUNCTIONS

 
2) Deniz A., Koçak S., Özdemir Y. and Üreyen A.E.: WALLPAPER PATTERNS WITH SELF-SIMILAR AND
GRAPH-DIRECTED FRACTAL LATTICE UNITS

 
3) Miller A.R.: FLUTED TUBES AND WAISTED CIRCLES

 
4) Rasmussen S.L.: COLORINGS OF PLANE PATTERNS DEFINED BY SEQUENCES AND
ARRAYS, INSPIRED BY WEAVING DESIGNS

 
5) Zefiro L.: VERTEX- AND EDGE-TRUNCATION OF THE PLATONIC AND ARCHIMEDEAN
SOLIDS LEADING TO VERTEX-TRANSITIVE POLYHEDRA

 
5) Zefiro L.: REGULAR-SHAPED FACES IN SOLIDS WITH CUBIC SYMMETRY DERIVED FROM
TRUNCATION PROCESS BY RHOMB_DODECAHEDRON OR CUBE

 
 



2012




Volume 14, No. 1, 2012 

 
1) Bodnar O.: MINKOWSKI GEOMETRY IN THE MATHEMATICAL MODELING OF NATURAL PHENOMENA

 
2) Zefiro L.: REGULAR-SHAPED FACES DERIVING FROM THE TRUNCATION OF SOLIDS WITH ICOSAHEDRAL SYMMETRY BY A RHOMB-TRIACONTAHEDRON



Volume 14, No. 2, 2012 

 
1) Nakamura S., Minematsu D., Kitagawa T., Naito Y., Fujii R., Hieda T. and Miyadera R.:
CHOCOLATE GAMES THAT ARE VARIANTS OF NIM AND INTERESTING GRAPHS MADE BY THIS GAMES

 
2) Ramachandram V.V.S.: DYNAMICS IN GROUPS

 
3) Stakhov A.: A GENERALIZATION OF THE CASSINI FORMULA



Volume 14, No. 3, 2012 

 
1)Gerdes, P.: A NUER DANCE RATTLE (SOUTH SUDAN) PLAITING AN OCTAHEDRAL SHAPE

 
2) Lazureanu, C.: ON THE CORDOVAN OGIVE

 

 

 

 


 


 

 
MathArt Info

 
VISUAL MATHEMATICS: CALL FOR PAPERS

 
 

 


Copyright by ISIS-Symmetry

COPYRIGHT STATEMENT

Educational institutions are encouraged to reproduce and distribute these materials for educational use free of charge as long as credit and notification are provided. For any other purpose except educational, such as commercial etc, use of these materials is prohibited without prior written permission. Readers may download papers for personal or educational use only, and not for any kind of commercial use. Illustrations can be used only as a part of the papers and by no means can be reused for any purpose without the permission of the owner of the copyrights. 


This publication was partially supported by the Hungarian Research Fund (OTKA) No. T 025993 grant.