2. 10-2A Frieze Patterns What is a frieze pattern? What is glide reflection? What is translation symmetry? How many different symmetry classifications are there for frieze patterns?

3. Frieze Pattern A frieze pattern is a strip design that repeats itself. Examples: Decorative borders Tracks made by tire treads Ancient Greek urns

4. Definition A frieze pattern is created by repeated translations of a pattern along a line. All of the frieze patterns we will work with will repeat horizontally. Many frieze designs will have line symmetry and rotational symmetry. Horizontal symmetry ΣΣΣΣΣΣΣΣΣΣΣΣΣ

5. Glide-Reflection Symmetry What is a glide reflection? A pattern defined by repeating a translation followed by a reflection. Line of reflection Translation vector

6. Does the pattern have glide reflection symmetry? Translation vector Line of reflection Yes

7. What is translational symmetry? The property that a figure coincides with itself after a translation.

8. Name all of the types of symmetry in each frieze pattern. 1. Translation, glide reflection, vertical line, point 2. Translation, vertical line 3. Translation

9. Classification of Frieze Patterns p. 690 Type of Symmetry (Translation sym plus) Example No other symmetryLLLLLLLLLLLLLLLLLLL Horizontal line symmetry CCCCCCCCCCCCCC Point symmetry Glide-reflection symmetry Vertical line symmetryΛ Λ Λ Λ Λ Λ Vertical line & glide-reflect Vertical and horizontal line‡‡‡‡‡‡‡‡‡‡‡‡‡‡‡‡‡‡

10. Symmetry Search 1.Each group will be given letters of the alphabet. 2.Using capital letters, sketch examples of frieze patterns for each letter. 3.Identify what types of symmetry each of your patterns has.

11. What is a frieze pattern? A frieze pattern is created by repeated translations of a pattern along a line. What is glide reflection? A pattern defined by repeating a translation followed by a reflection. What is translation symmetry? The property that a figure coincides with itself after a translation. How many different symmetry classifications are there for frieze patterns? Seven (7)

12. Assignment 10-2A Page 691, 1-8, 10-13, 24-30