Course:Harris, Fall 08: Diary Week 12

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  • We confirmed one week from today as the date for Exam 2.
  • I explained my (current) scheme for grading the Art Project (artistic porition)
    • Artistic Vision
      • 10 max (average: 10): adherence to basic requirements
        • recognizable figures
        • no background between figures
        • no overlapping of one figure by another
      • 10 max (average: 5): inherent interest or complexity of the pattern
      • 3 max (average: 0): bonus for cleverness of motif or theme
    • Artistic Execution
      • 3 max (average: 2): appropriateness of choice of medium
      • 6 max (average: 3): technique of application of medium
      • 5 max (average: 4): accuracy of repetition of figures
      • 6 max (average: 3): details of outlines of figures
      • 6 max (average: 3): detailing interior of figures
      • 3 max (average: 0): bonus for overall impressiveness
    • Thus, the average project (say, mid-B) will get about 30 points; the maximum possible is 52 (that would be for Escher himself).
  • We finished up spherical tessellations:
    • We know we can have any number of biangles in a regular tessellation.
    • For more "normal" polygons, we found these as the only possibles:
      • 4 triangles, 3 at a vertex
      • 8 triangles, 4 at a vertex
      • 20 triangles, 5 at a vertex
      • 6 squares, 3 at a vertex
      • 12 pentagons, 3 at vertex
    • But are those actually realizable on the sphere?
      • We used KaleidoTile to find that, yes, they are each actually spherical tessellations.
      • We also used KaleidoTile to look at the corresponding Euclidean solid tessellations:
        • tetrahedron
        • octahedron
        • icosahedron
        • cube
        • dodecahedron
  • We spent the last 15 minutes with groups doing the Hyperbolic Geometry Exploration.


  • Exam II preparation:
    • Practicing drawing a tessellation with a non-convex quadrilateral is a good idea.
    • For showing why there are only so many regular tessellations (for plane or sphere), the key is to first look at polygons fitting around a vertex.
  • We took about 40 minutes to do Hyperbolic Exploration in Non-Euclid.
  • I amended the Exercise assignment (Hyperbolic II) to leave out dual tessellations and finding areas of the basic polygons in Circle I and II.