{"id":103,"date":"2014-09-30T13:58:00","date_gmt":"2014-09-30T18:58:00","guid":{"rendered":"https:\/\/pages.stolaf.edu\/cederj\/?page_id=103"},"modified":"2015-08-05T16:33:00","modified_gmt":"2015-08-05T21:33:00","slug":"symmetry","status":"publish","type":"page","link":"https:\/\/pages.stolaf.edu\/cederj\/symmetry\/","title":{"rendered":"Symmetry"},"content":{"rendered":"

<\/h1>\n
    \n
  1. Ackroyd, Peter\u00a0Blake<\/i>, Sinclair-Stevenson, 1995. PR4147.A55<\/li>\n
  2. Armstrong, M.A.\u00a0Groups and Symmetry<\/i>, Springer-Verlag, 1988 (Loren)<\/li>\n
  3. Ascher, Marcia: “Patterned Strip Decorations”, Chapter 7 in\u00a0Ethnomathatics: Mathematical Ideas in Other Cultures.<\/i>, Wadsworth & Brooks\/Cole, 1990.<\/li>\n
  4. Baglivo, Jenny A.\u00a0Incidence and Symmetry in Design and Architecture\u00a0<\/i>, NA2750 .B3<\/li>\n
  5. Barber, Frederick, et al.,\u00a0Tiling the Plane<\/i>, COMAP Module, 1989.<\/li>\n
  6. Boles & Newman,\u00a0The Surface Plane<\/i>\u00a0, Pythagorean Press, 1992. (JNC)<\/li>\n
  7. Brown, Richard G.\u00a0Transformation Geometry<\/i>, Dale Seymour, 1973 (JNC)<\/li>\n
  8. Buyske, Cederberg, Magariar, Simonson,\u00a0Tilings, Periodic & Penrose<\/i>, COMAP Module.<\/li>\n
  9. Caldwell, J.H.\u00a0Topics in Recreational Mathematics<\/i>, Cambridge University Press, 1966 (Chapter 11) (JNC – xeroxed copy).<\/li>\n
  10. Clason, R., Peters, W., Frank, M., “Quasicrystals and the Penrose Patterns: A Geometric Activity with a Scientific Application,” in\u00a0School Science and Mathematics<\/i>, Vol 93(7), November 1993.<\/li>\n
  11. COMAP,\u00a0Geometry’s Future<\/i>, Conference Proceedings sponsored by COMAP.<\/li>\n
  12. Coxeter,\u00a0Introduction to Geometry<\/i><\/li>\n
  13. Coxeter & Moser,\u00a0Generators & Relations for Discrete Groups<\/i>, 4th ed QA171.C7<\/li>\n
  14. Crowe, Donald\u00a0Symmetry, Rigid Motions, and Patterns<\/i>, HIMAP Module 4, COMAP, 1986. (JNC)<\/li>\n
  15. Devlin, Keith “Symmetry and Regularity” in\u00a0Mathematics: The Science of Patterns<\/i>, Scientific American Library (Steen, JNC)<\/li>\n
  16. Dubrovsky, Vladimir, “Ornamental Groups”, in\u00a0Quantum<\/i>\u00a0November\/December 1991.<\/li>\n
  17. Ehrenfeucht, A.\u00a0The Cube Made Interesting<\/i>, Pergamon Press, 1964 (Martha)<\/li>\n
  18. Ernst, Bruno,\u00a0The Magic Mirror of M. C. Escher<\/i>\u00a0(JNC)<\/li>\n
  19. Farmer, David\u00a0Groups and Symmetry: A Guide to Discovering Mathematics<\/i>, AMS 1996.<\/li>\n
  20. Fejes Toth L.,\u00a0Regular Figures<\/i>\u00a0QA601.F38<\/li>\n
  21. Fetter, Ann et al.\u00a0Three-Dimensional Symmetry Activity Book<\/i>, Key Curriculum Press. Has a great bibliography and an accompanying video.<\/li>\n
  22. Field, Michael and Golubitsky, Martin,\u00a0Symmetry in Chaos: A Search For Pattern in Mathematics and Nature<\/i>, Oxford, 1992. (Wallace)<\/li>\n
  23. Gallian, Joseph A.,\u00a0Contemporary Abstract Algebra,<\/i>\u00a0(3rd. ed.), Heath 1994.<\/li>\n
  24. Gallian, Joseph A., “Symmetry in Logos and Hubcaps” in\u00a0American Mathematical Monthly<\/i>\u00a097(3):235-238, March 1990.<\/li>\n
  25. Gardner, Martin, “The Art of M. C. Escher”\u00a0Mathematical Carnival<\/i><\/li>\n
  26. Gardner, Martin,\u00a0Penrose Tiles to Trapdoor Ciphers<\/i>\u00a0W.H. Freeman, 1989.<\/li>\n
  27. Garfunkel et al., “Patterns”, Chapter 17 in\u00a0For All Practical Purposes<\/i>, Freeman. (Steen)<\/li>\n
  28. Grunbaum & Shephard,\u00a0Tilings and Patterns,<\/i>, QA166.8.G78<\/li>\n
  29. Hanson, Robert M.\u00a0Molecular Origami<\/i>. (JNC)<\/li>\n
  30. Hargittai and Hargittai,\u00a0Symmetry: A Unifying Concept<\/i>, Shelter, 1994. (JNC)<\/li>\n
  31. Hargittai and Lengyel, “The Seven One-Dimensional Space-Group Symmetries Illustrated by Hungarian Folk Needlework,”\u00a0J. Chemical Education<\/i>, Dec. `84<\/li>\n
  32. Hargittai and Lengyel, “The Seventeen Two-Dimensional Space-Group Symmetries in Hungarian Needlework”,\u00a0J. Chemical Education<\/i>, Jan. `85<\/li>\n
  33. Henle, Michael,\u00a0Modern Geometries: The Analytic Approach<\/i>, Prentice Hall, 1997 (JNC)<\/li>\n
  34. Holden, Alan\u00a0Shapes, Space and Symmetry<\/i>, Dover, 1973. QA491.H63<\/li>\n
  35. Locher, J.L.,\u00a0The World of M. C. Escher<\/i><\/li>\n
  36. Lockwood, E.H., and MacMillan, R.H.~\u00a0Geometric Symmetry<\/i>, 1977 (Smith)<\/li>\n
  37. NCTM,\u00a0Connecting Mathematics<\/i>, Addenda Series: Grades 9-12, 1991 (JNC)<\/li>\n
  38. NCTM,\u00a0Geometry From Multiple Perspectives<\/i>, Addenda Series: Grades 9-12, 1991 (JNC)<\/li>\n
  39. MacGillavry, Caroline H.,\u00a0Symmetry Aspects of M. C. Escher’s Periodic Drawings<\/i>, NC745.M3<\/li>\n
  40. McKeown and Badler, “Creating Polyhedral Stellations,”\u00a0Computer Graphics<\/i>, July `80<\/li>\n
  41. Natsoulas, Anthula, “Group Symmetries Connect Art and History with Mathematics,”\u00a0Mathematics Teacher<\/i>\u00a093:5 (May 2000): 364-370<\/li>\n
  42. Niman & Norman, “Mathematics and Islamic Art,”\u00a0The American Mathematical Monthly<\/i>, Vol 8, June-July `78<\/li>\n
  43. O`Daffer,\u00a0Geometry: An Investigative Approach<\/i>, QA445.042<\/li>\n
  44. Paley, Morton D.,\u00a0William Blake<\/i>, Phaidon, 1978 PR4147.P35<\/li>\n
  45. Penrose, Roger:\u00a0The Emperor’s New Mind<\/i>, Oxford University Press, 1989.<\/li>\n
  46. Ranucci, Ernest R., “Master of Tessellations: M. C. Escher 1898-1972,”\u00a0The Mathematics Teacher<\/i>, April `74, Vol 64, #4, p 229-306<\/li>\n
  47. Ranucci, E.R. & Teeters, J.E., “Creating Escher-Type Drawings,”\u00a0The Mathematics Teacher<\/i>\u00a0April `74, Vol 64, #4?<\/li>\n
  48. Rose, B. and Stafford, R., “An Elementary Course in Mathematical Symmetry” in\u00a0The American Mathematical Monthly<\/i>\u00a088 (1981): 59-64.<\/li>\n
  49. Rosen, Joe,\u00a0Symmetry in Science: An Introduction to the General Theory<\/i>, Springer, 1995. (Martha)<\/li>\n
  50. Rush, Jean, “On the Appeal of M. C. Escher’s Pictures,”\u00a0Leonardo<\/i>\u00a012 (79)<\/li>\n
  51. Schattschneider, Doris, “Tiling the Plane with Congruent Pentagons,”\u00a0Mathematics Magazinei<\/i>, Jan `78<\/li>\n
  52. Schattschneider, Doris, “Plane Symmetry Groups,”\u00a0Mathematical Monthly<\/i>, (85) June-July `78<\/li>\n
  53. Schattschneider, Doris, “The Plane Symmetry Groups: Their Recognition and Notation,”\u00a0Mathematical Monthly<\/i>, `85 (`78)<\/li>\n
  54. Schattschneider, Doris, “Will It Tile? Try the Conway Criterion!,”\u00a0Mathematics Magazine<\/i>, Sept `80<\/li>\n
  55. Schattschneider Doris,\u00a0Visions of Symmetry: Notebooks, Periodic Drawings and Related Works of M. C. Escher<\/i>, W. H. Freeman `90 (JNC)<\/li>\n
  56. Senechal, Marjorie “Which Tetrahedra Fill Space?,”\u00a0Mathematics Magazine<\/i>\u00a0Nov `81<\/li>\n
  57. Senechal, Marjorie and Fleck, George\u00a0Patterns of Symmetry<\/i>\u00a01974. (Smith)<\/li>\n
  58. Senechal, Marjorie, “Finding the Finite Groups of Symmetries of the Sphere” in\u00a0The American Mathematical Monthly<\/i>\u00a097 (1990): 329-335.<\/li>\n
  59. Senechal, Marjorie and Jean Taylor, “Quasicrystals:The View from Les Houches” in\u00a0Mathematical Intelligencer<\/i>\u00a012(2):54-64 (Spring 1990).<\/li>\n
  60. Seymour, Dale & Britton, Jill,\u00a0Introduction to Tessellations<\/i>, p 183-236, Dale Seymour Publications<\/li>\n
  61. Shubnikov and Koptsik,\u00a0Symmetry in Science And Art<\/i>, Plenum, 1964 (Loren)<\/li>\n
  62. Sibley, Thomas Q.\u00a0Geometric Patterns: A Study in Symmetry<\/i>, Saint John’s University, 1989. (JNC)<\/li>\n
  63. Steen,\u00a0On the Shoulders of Giants: New Approaches to Numeracy<\/i>, National Research Council, 1990.<\/li>\n
  64. Steinhardt, Paul Joseph: “Quasicrystals” in\u00a0American Scientist,<\/i>\u00a074(6):586-597 (Nov.-Dec. 1986)<\/li>\n
  65. Stewart, Ian and Golubitsky, Martin,\u00a0Fearful Symmetry: Is God a Geometer?<\/i>, Penguin, 1992.<\/li>\n
  66. Tannenbaum Peter & Robert Arnold, Chapter 11 (Symmetry of Motion) and Chapter 12 (Symmetry of Scale and Fractals) in\u00a0Excursions In Modern Mathematics<\/i>, 2nd ed., Prentice Hall 1995. (Bolstad)<\/li>\n
  67. Teeters, Joseph C. “How To Draw Tessellations of the Escher Type,”\u00a0The Mathematics Teacher<\/i>, April `74, Vol 64, #4, p 307-310<\/li>\n
  68. von Baeyer, H. “Impossible Crystals” in\u00a0Discover<\/i>\u00a011 (2) (1990): 69-78.<\/li>\n
  69. Washburn, Dorthy K., and Donald W. Crowe\u00a0Symmetries of Culture: Theory and Practice of Plane Pattern Analysis<\/i>, University of Washington Press 1988. Section 1.4 deals with the role of symmetry in perception.(JNC)<\/li>\n
  70. Weyl, Hermann,\u00a0Symmetry<\/i>\u00a0(JNC)<\/li>\n
  71. Yale, Paul\u00a0Geometry and Symmetry<\/i>, Dover (JNC)<\/li>\n
  72. Zaslavsky, Claudia\u00a0Africa Counts; number and pattern in African culture<\/i>\u00a0GN476.1.Z37<\/li>\n<\/ol>\n

    Software For Use In Symmetry Exploration:<\/h3>\n
      \n
    1. Cabri Geometry (Texas Instruments)<\/li>\n
    2. DiscoverForm (Intellimation)<\/li>\n
    3. Escher-Sketch (Intellimation)<\/li>\n
    4. The Geometer’s Sketchpad (Key Curriculum Press)<\/li>\n
    5. Geometric Golfer (MECC)<\/li>\n
    6. Kaleidotile (ftp.geom.umn.edu)<\/li>\n
    7. Kali (ftp.geom.umn.edu)<\/li>\n
    8. Tesselmania (MECC)<\/li>\n<\/ol>\n

      Videos For Use in Symmetry Exploration<\/h3>\n
        \n
      1. The Alahambra Past and Present—A Geometer’s Odyssey<\/i>, Parts I and II, California State University, Northridge, 1992.<\/li>\n
      2. Dihedral Kaleidoscopes<\/i>, College Geometry Project, 1966. (owned by St. Olaf)<\/li>\n
      3. Symmetries of the Cube<\/i>, College Geometry Project, 1971 (owned by St. Olaf)<\/li>\n
      4. Three Dimensional Symmetry<\/i>, Key Curriculum Press, 1994. (owened St. Olaf)<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

        Ackroyd, Peter\u00a0Blake, Sinclair-Stevenson, 1995. PR4147.A55 Armstrong, M.A.\u00a0Groups and Symmetry, Springer-Verlag, 1988 (Loren) Ascher, Marcia: “Patterned Strip Decorations”, Chapter 7 in\u00a0Ethnomathatics: Mathematical Ideas in Other Cultures., Wadsworth & Brooks\/Cole, 1990. Baglivo, Jenny A.\u00a0Incidence and Symmetry in Design and Architecture\u00a0, NA2750 .B3 Barber, Frederick, et al.,\u00a0Tiling the Plane, COMAP Module, 1989. Boles & Newman,\u00a0The Surface Plane\u00a0, Pythagorean […]<\/p>\n","protected":false},"author":841,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-103","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/pages\/103","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/users\/841"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/comments?post=103"}],"version-history":[{"count":2,"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/pages\/103\/revisions"}],"predecessor-version":[{"id":291,"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/pages\/103\/revisions\/291"}],"wp:attachment":[{"href":"https:\/\/pages.stolaf.edu\/cederj\/wp-json\/wp\/v2\/media?parent=103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}