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. 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

 

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

 

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

 

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

 

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

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

 
 

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

 
 

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