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7.6 Frieze Patterns

7.6 Frieze Patterns. Geometry Mrs. Spitz Spring 2010. What You Should Learn Why You Should Learn It. How to use transformations to classify frieze patterns How to use frieze patterns in real life

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7.6 Frieze Patterns

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  1. 7.6 Frieze Patterns Geometry Mrs. Spitz Spring 2010

  2. What You Should LearnWhy You Should Learn It • How to use transformations to classify frieze patterns • How to use frieze patterns in real life • You can use frieze patterns to create decorative borders for real-life objects such as fabric, pottery, and buildings

  3. Assignment • pp. 440-441 #1-31 all

  4. Classifying Frieze Patterns • A frieze pattern or strip pattern is a pattern that extends infinitely to the left and right in such a way that the pattern can be mapped onto itself by a horizontal translation • Some frieze patterns can be mapped onto themselves by other transformations: • A 180° rotation • A reflection about a horizontal line • A reflection about a vertical line • A horizontal glide reflection

  5. Example 1Examples of Frieze Patterns • Name the transformation that results in the frieze pattern

  6. Name the transformation that results in the frieze pattern Horizontal Translation Horizontal Translation Or 180° Rotation Horizontal Translation Or Reflection about a vertical line Horizontal Translation Or Horizontal glide reflection

  7. Frieze Patterns in Real-Life

  8. 7 Categories of Frieze Patterns

  9. Classifying Frieze PatternsUsing a Tree Diagram

  10. Example 2Classifying Frieze Patterns • What kind of frieze pattern is represented?

  11. Example 2Classifying Frieze Patterns • What kind of frieze pattern is represented? • TRHVG • It can be mapped onto itself by a translation, a 180° rotation, a reflection about a horizontal or vertical line, or a glide reflection

  12. Example 3Classifying a Frieze Pattern A portion of the frieze pattern on the above building is shown. Classify the frieze pattern. TRHVG

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