1. SYMMETRY: Theory, Reality and Art! A GEMS/ALEX Submission Submitted by: Elizabeth Thompson, PhD. Summer, 2008

2. Types of Symmetry Rotation Translation Reflection

3. Rotational Symmetry Illustration: http://mathforum.org/sum95/suzanne/symsusan.html Take an object and rotate it by some degree (90, 45, 180, 26) and you have an example of rotational symmetry) Every rotation has a center and an angle!

4. Examples of Rotational Symmetry Can you find the center of each object, and approximate the degrees that each object was rotated? (click for each) What other objects would have rotational symmetry?

5. Translational Symmetry Illustration: http://mathforum.org/sum95/suzanne/symsusan.html Every translation has a distance and a direction. Translations are not rotated or reflected…the shape remains the same size.

6. Examples of Translational Symmetry The objects simply move from one position to another retaining size and shape.

7. Reflective Symmetry Illustration: http://mathforum.org/sum95/suzanne/symsusan.html Every reflection has a line of reflection (a mirror line).

8. Examples of Reflective Symmetry Can you find the line of reflection in each object? (click to see)

9. Multiple forms of symmetry can be found in one object…can you name the ones found here? The flower has rotational and/or reflective symmetry. The Escher Art has reflective…then it is translated (that makes it a tessellation)

10. POWERPOINT BREAK TIME FOR PRACTICE (see teacher notes)

11. PART TWO: Tessellations (Geometric Art) "I never got a pass mark in math... Just imagine -- mathematicians now use my prints to illustrate their books." -- M.C. Escher

12. Samples of tessellations

13. How to Tessellate (Slide 1 of 3) (there are many methods…this is just one)

14. How to Tessellate (Slide 2 of 3)

15. How to Tessellate (Slide 3 of 3)

16. Student Samples (repeated) Warning: These are harder than they appear… frustration levels can rise.