Symmetry up previous
Next: About this document ... Up: Index of Topics Previous: Golden Ratio

Symmetry

  1. Ackroyd, Peter Blake, Sinclair-Stevenson, 1995. PR4147.A55
  2. Armstrong, M.A. Groups and Symmetry, Springer-Verlag, 1988 (Loren)
  3. Ascher, Marcia: ``Patterned Strip Decorations'', Chapter 7 in Ethnomathatics: Mathematical Ideas in Other Cultures., Wadsworth & Brooks/Cole, 1990.
  4. Baglivo, Jenny A. Incidence and Symmetry in Design and Architecture , NA2750 .B3
  5. Barber, Frederick, et al., Tiling the Plane, COMAP Module, 1989.
  6. Boles & Newman, The Surface Plane , Pythagorean Press, 1992. (JNC)
  7. Brown, Richard G. Transformation Geometry, Dale Seymour, 1973 (JNC)
  8. Buyske, Cederberg, Magariar, Simonson, Tilings, Periodic & Penrose, COMAP Module.
  9. Caldwell, J.H. Topics in Recreational Mathematics, Cambridge University Press, 1966 (Chapter 11) (JNC - xeroxed copy).
  10. Clason, R., Peters, W., Frank, M., ``Quasicrystals and the Penrose Patterns: A Geometric Activity with a Scientific Application,'' in School Science and Mathematics, Vol 93(7), November 1993.
  11. COMAP, Geometry's Future, Conference Proceedings sponsored by COMAP.
  12. Coxeter, Introduction to Geometry
  13. Coxeter & Moser, Generators & Relations for Discrete Groups, 4th ed QA171.C7
  14. Crowe, Donald Symmetry, Rigid Motions, and Patterns, HIMAP Module 4, COMAP, 1986. (JNC)
  15. Devlin, Keith ``Symmetry and Regularity'' in Mathematics: The Science of Patterns, Scientific American Library (Steen, JNC)
  16. Dubrovsky, Vladimir, ``Ornamental Groups'', in Quantum November/December 1991.
  17. Ehrenfeucht, A. The Cube Made Interesting, Pergamon Press, 1964 (Martha)
  18. Ernst, Bruno, The Magic Mirror of M. C. Escher (JNC)
  19. Farmer, David Groups and Symmetry: A Guide to Discovering Mathematics, AMS 1996.
  20. Fejes Toth L., Regular Figures QA601.F38
  21. Fetter, Ann et al. Three-Dimensional Symmetry Activity Book, Key Curriculum Press. Has a great bibliography and an accompanying video.
  22. Field, Michael and Golubitsky, Martin, Symmetry in Chaos: A Search For Pattern in Mathematics and Nature, Oxford, 1992. (Wallace)
  23. Gallian, Joseph A., Contemporary Abstract Algebra, (3rd. ed.), Heath 1994.
  24. Gallian, Joseph A., ``Symmetry in Logos and Hubcaps'' in American Mathematical Monthly 97(3):235-238, March 1990.
  25. Gardner, Martin, ``The Art of M. C. Escher'' Mathematical Carnival
  26. Gardner, Martin, Penrose Tiles to Trapdoor Ciphers W.H. Freeman, 1989.
  27. Garfunkel et al., ``Patterns'', Chapter 17 in For All Practical Purposes, Freeman. (Steen)
  28. Grunbaum & Shephard, Tilings and Patterns,, QA166.8.G78
  29. Hanson, Robert M. Molecular Origami. (JNC)
  30. Hargittai and Hargittai, Symmetry: A Unifying Concept, Shelter, 1994. (JNC)
  31. Hargittai and Lengyel, ``The Seven One-Dimensional Space-Group Symmetries Illustrated by Hungarian Folk Needlework,'' J. Chemical Education, Dec. `84
  32. Hargittai and Lengyel, ``The Seventeen Two-Dimensional Space-Group Symmetries in Hungarian Needlework'', J. Chemical Education, Jan. `85
  33. Henle, Michael, Modern Geometries: The Analytic Approach, Prentice Hall, 1997 (JNC)
  34. Holden, Alan Shapes, Space and Symmetry, Dover, 1973. QA491.H63
  35. Locher, J.L., The World of M. C. Escher
  36. Lockwood, E.H., and MacMillan, R.H.~ Geometric Symmetry, 1977 (Smith)
  37. NCTM, Connecting Mathematics, Addenda Series: Grades 9-12, 1991 (JNC)
  38. NCTM, Geometry From Multiple Perspectives, Addenda Series: Grades 9-12, 1991 (JNC)
  39. MacGillavry, Caroline H., Symmetry Aspects of M. C. Escher's Periodic Drawings, NC745.M3
  40. McKeown and Badler, ``Creating Polyhedral Stellations,'' Computer Graphics, July `80
  41. Natsoulas, Anthula, ``Group Symmetries Connect Art and History with Mathematics,'' Mathematics Teacher 93:5 (May 2000): 364-370
  42. Niman & Norman, ``Mathematics and Islamic Art,'' The American Mathematical Monthly, Vol 8, June-July `78
  43. O`Daffer, Geometry: An Investigative Approach, QA445.042
  44. Paley, Morton D., William Blake, Phaidon, 1978 PR4147.P35
  45. Penrose, Roger: The Emperor's New Mind, Oxford University Press, 1989.
  46. Ranucci, Ernest R., ``Master of Tessellations: M. C. Escher 1898-1972,'' The Mathematics Teacher, April `74, Vol 64, #4, p 229-306
  47. Ranucci, E.R. & Teeters, J.E., ``Creating Escher-Type Drawings,'' The Mathematics Teacher April `74, Vol 64, #4?
  48. Rose, B. and Stafford, R., ``An Elementary Course in Mathematical Symmetry'' in The American Mathematical Monthly 88 (1981): 59-64.
  49. Rosen, Joe, Symmetry in Science: An Introduction to the General Theory, Springer, 1995. (Martha)
  50. Rush, Jean, ``On the Appeal of M. C. Escher's Pictures,'' Leonardo 12 (79)
  51. Schattschneider, Doris, ``Tiling the Plane with Congruent Pentagons,'' Mathematics Magazinei, Jan `78
  52. Schattschneider, Doris, ``Plane Symmetry Groups,'' Mathematical Monthly, (85) June-July `78
  53. Schattschneider, Doris, ``The Plane Symmetry Groups: Their Recognition and Notation,'' Mathematical Monthly, `85 (`78)
  54. Schattschneider, Doris, ``Will It Tile? Try the Conway Criterion!,'' Mathematics Magazine, Sept `80
  55. Schattschneider Doris, Visions of Symmetry: Notebooks, Periodic Drawings and Related Works of M. C. Escher, W. H. Freeman `90 (JNC)
  56. Senechal, Marjorie ``Which Tetrahedra Fill Space?,'' Mathematics Magazine Nov `81
  57. Senechal, Marjorie and Fleck, George Patterns of Symmetry 1974. (Smith)
  58. Senechal, Marjorie, ``Finding the Finite Groups of Symmetries of the Sphere'' in The American Mathematical Monthly 97 (1990): 329-335.
  59. Senechal, Marjorie and Jean Taylor, ``Quasicrystals:The View from Les Houches'' in Mathematical Intelligencer 12(2):54-64 (Spring 1990).
  60. Seymour, Dale & Britton, Jill, Introduction to Tessellations, p 183-236, Dale Seymour Publications
  61. Shubnikov and Koptsik, Symmetry in Science And Art, Plenum, 1964 (Loren)
  62. Sibley, Thomas Q. Geometric Patterns: A Study in Symmetry, Saint John's University, 1989. (JNC)
  63. Steen, On the Shoulders of Giants: New Approaches to Numeracy, National Research Council, 1990.
  64. Steinhardt, Paul Joseph: ``Quasicrystals'' in American Scientist, 74(6):586-597 (Nov.-Dec. 1986)
  65. Stewart, Ian and Golubitsky, Martin, Fearful Symmetry: Is God a Geometer?, Penguin, 1992.
  66. Tannenbaum Peter & Robert Arnold, Chapter 11 (Symmetry of Motion) and Chapter 12 (Symmetry of Scale and Fractals) in Excursions In Modern Mathematics, 2nd ed., Prentice Hall 1995. (Bolstad)
  67. Teeters, Joseph C. ``How To Draw Tessellations of the Escher Type,'' The Mathematics Teacher, April `74, Vol 64, #4, p 307-310
  68. von Baeyer, H. ``Impossible Crystals'' in Discover 11 (2) (1990): 69-78.
  69. Washburn, Dorthy K., and Donald W. Crowe Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, University of Washington Press 1988. Section 1.4 deals with the role of symmetry in perception.(JNC)
  70. Weyl, Hermann, Symmetry (JNC)
  71. Yale, Paul Geometry and Symmetry, Dover (JNC)
  72. Zaslavsky, Claudia Africa Counts; number and pattern in African culture GN476.1.Z37

Software For Use In Symmetry Exploration:

  1. Cabri Geometry (Texas Instruments)
  2. DiscoverForm (Intellimation)
  3. Escher-Sketch (Intellimation)
  4. The Geometer's Sketchpad (Key Curriculum Press)
  5. Geometric Golfer (MECC)
  6. Kaleidotile (ftp.geom.umn.edu)
  7. Kali (ftp.geom.umn.edu)
  8. Tesselmania (MECC)

Videos For Use in Symmetry Exploration

  1. The Alahambra Past and Present---A Geometer's Odyssey, Parts I and II, California State University, Northridge, 1992.
  2. Dihedral Kaleidoscopes, College Geometry Project, 1966. (owned by St. Olaf)
  3. Symmetries of the Cube, College Geometry Project, 1971 (owned by St. Olaf)
  4. Three Dimensional Symmetry, Key Curriculum Press, 1994. (owened St. Olaf)

Judith Cederberg

Disclaimer