Supplementary Investigation 9

Other Frieze Patterns

Tool(s) Geometers Sketchpad

Data File(s) si9

Focus Each frieze pattern has a different set of symmetries.

Tasks

1. Pattern F¹₁ has the center line as a line of symmetry but no points of symmetry, like the pattern DDDDDD. Construct a frieze based on this pattern.

2. Pattern F²₁ has a line of symmetry perpendicular to the centerline at the midpoint, like the pattern VVVVVV. Construct a frieze based on this pattern.

3. Pattern F¹₂ is symmetric about the center line and has a point of symmetry at the midpoint, like the pattern HHHHHH. Construct a frieze based on this pattern.

4. Pattern F²₂ is symmetric about a line perpendicular to the centerline 1/4 of the width of the box from the left edge and a point of symmetry at the midpoint, like the pattern. Construct a frieze based on this pattern.

5. Pattern F³₁ is a glide reflection. Construct a frieze based on this pattern.

6. Examine stationary samples for boarders that are frieze patterns. Classify each into one of the seven frieze patterns.

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