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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 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

 




 
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

 
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


 

 

 
 

 
MathArt Info

 
VISUAL MATHEMATICS: CALL FOR PAPERS

 
IN THE NEXT ISSUE

 
 

 


Copyright by ISIS-Symmetry

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