1. 1 Chapter 9 Transformations and Design

2. 2 Objectives of the Chapter  Relate transformations to symmetry and design in logos  Analyze the geometric aspects of logos and other designs  Investigate the effects of geometric transformations using technology  Create a personal logo involving symmetry and transformation using technology  Investigate the characteristics of shapes that tile a plane  Create designs involving tiling patterns using technology

3. 3 The Big Picture  Design a business  Create a logo (applying principles from chapter)  Design a product for your business

4. 4 Transformations Rotations Turning a figure around a point Translations Slides objects up or down, left or right Dilatations Enlarges or reduces an object Reflections Flipping a figure over a line (mirror image)

5. 5 Activity 1: The VVWA Verbal and Visual Word Association is a reading strategy for learning new vocabulary terms WordVisual Verbal = definition Personal Association Website: http://www.intermath-uga.gatech.edu/dictnary/homepg.asphttp://www.intermath-uga.gatech.edu/dictnary/homepg.asp

6. 6 Using Dynamic Geometry Software Geometer sketchpad Winplot (http://math.exeter.edu/rparris/winplot.html)http://math.exeter.edu/rparris/winplot.html Simple graphing program: http://www.serpik.com/agrapher/ http://www.serpik.com/agrapher/ Autograph

7. 7 Designing a Logo Points to remember Keep it clean and simple Font Thick = strength and power Script = elegance Slant = movement Colour Blue, maroon, dark teal = conservative Black and white = contemporary

8. 8 Designing a Logo Software cites to look at: Logo design software: http://www.aaa-logo.comhttp://www.aaa-logo.com Microsoft Photodraw CorelDraw (http://www.corel.com)http://www.corel.com Adobe Illustrator and Adobe Photoshop (http://www.adobe.com/support/downloads)http://www.adobe.com/support/downloads Macromedia Freehand or Flash (http://www.macromedia.com/downloads/)http://www.macromedia.com/downloads/ Drawing program: http://www.drawinghand.com/http://www.drawinghand.com/

9. 9 Tiling a Plane To tile a plane is to place shapes edge to edge to cover a flat surface without spaces or overlap. The ancient Greek word tesserae (tessellate) stands for the square blocks used in tiling. A repeating arrangement of shapes that completely covers a plane, with no gaps and no overlaps, is called a tessellation.

10. 10 What is a tiling? Tilings or tessellations are coverings of the plane with tiles.

11. 11 Most Famous: Escher “To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of art.” ~M.C. Escher Escher was the most famous artist with respect to tessellations

12. 12 Two types of activities 1. hands on (using materials) † Be creative 2. software (Tessellation Exploration) † 8 activities to follow that cover everything in the chapter (and then some) plus a quiz on symmetry and transformations (Activity 2)