Course:Harris, Fall 08: Diary Week 12

Mon:

• 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.

Wed:

• 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.