Difference between revisions of "Frieze Marking Exploration"
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===Procedure=== | ===Procedure=== | ||
| − | + | * Cut the transparency into eight strips as indicated. | |
| − | + | * First test for vertical and horizontal reflection symmetry. You can fold up the paper and check if there is a match. | |
| − | + | * For each strip pattern on the paper, use the corresponding transparency strip as an overlay to test for the remaining symmetries: | |
| + | ** Test for glide-reflections: Can you make the frieze pattern match up if you reflect the trip and slide it horizontally? | ||
| + | ** Test for rotational symmetry: Does the frieze look the same if you turn it through 180 degrees? | ||
| − | {{Handin|The paper of strip patterns, marked with symmetries.}} | + | |
| + | Answer the following questions: | ||
| + | |||
| + | <ol> | ||
| + | <li> On the paper, mark all symmetries for each pattern: | ||
| + | <ol style="list-style-type:lower-alpha"> | ||
| + | <li> Mark the length of the translation. | ||
| + | <li> Mark any reflectional symmetry by drawing the mirror lines. | ||
| + | <li> If there is a glide reflection, mark the length of the translation and label that arrow with a G. | ||
| + | <li> Mark any centers of rotation with a diamond. | ||
| + | </ol> | ||
| + | <li> Identify the frieze group for each pattern. | ||
| + | <li> What is going on with pattern #8? | ||
| + | </ol> | ||
| + | |||
| + | {{Handin|The paper of strip patterns, marked with symmetries and the frieze groups.}} | ||
[[category:Symmetry and Isometry Explorations]] | [[category:Symmetry and Isometry Explorations]] | ||
Revision as of 17:09, 30 August 2009
Objective: Learn to recognize symmetries of frieze patterns.
Materials
- Two copies of File:Blocky.pdf, one printed on paper and one on a transparency.
- Scissors
Procedure
- Cut the transparency into eight strips as indicated.
- First test for vertical and horizontal reflection symmetry. You can fold up the paper and check if there is a match.
- For each strip pattern on the paper, use the corresponding transparency strip as an overlay to test for the remaining symmetries:
- Test for glide-reflections: Can you make the frieze pattern match up if you reflect the trip and slide it horizontally?
- Test for rotational symmetry: Does the frieze look the same if you turn it through 180 degrees?
Answer the following questions:
- On the paper, mark all symmetries for each pattern:
- Mark the length of the translation.
- Mark any reflectional symmetry by drawing the mirror lines.
- If there is a glide reflection, mark the length of the translation and label that arrow with a G.
- Mark any centers of rotation with a diamond.
- Identify the frieze group for each pattern.
- What is going on with pattern #8?
Handin: The paper of strip patterns, marked with symmetries and the frieze groups.
