1. Transformations and Design
Chapter 9
Transformations and Design

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. The Big Picture Design a business
Create a logo (applying principles from chapter)
Design a product for your business
Bottom up vs. top down approach to learning (Wiggins)

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

5. Website: http://www.intermath-uga.gatech.edu/dictnary/homepg.asp
Activity 1: The VVWA
Verbal and Visual Word Association is a reading strategy for learning new vocabulary terms
Word
Visual
Verbal and Visual Word Association strategy uses a grid to organize new vocabulary and connect it to a visual that you can use to help you remember the terms.
Verbal =
definition
Personal
Association
Website:

6. Using Dynamic Geometry Software
Geometer sketchpad
Winplot (
Simple graphing program:
Autograph
Geometers sketchpad and autograph both cost money. Autograph has a 30 day free download after you sign up for an account. Sketchpad is on the book bureau list.
Winplot is a very cool program to do the work required for section 10.2.

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. Designing a Logo Software cites to look at:
Logo design software:
Microsoft Photodraw
CorelDraw (
Adobe Illustrator and Adobe Photoshop (
Macromedia Freehand or Flash (
Drawing program:
Cite 1 is a very cool program that takes about 48 seconds to download and installs onto the hard drive. It is free and works on windows 95/98/ME and XP. It is freeware.
Microsoft PhotoDraw is part of the office package.
Both the coral and the adobe programs are available for trial use but you must set up an account first (cumbersome)
Macromedia is very cool with available tutorials and is also available for free 30 day trials.
The last cite is a more advanced freehand drawing program that installs on your hard drive and loads in about 58 seconds. It is very cool if you have budding artists in your class. It is freeware.

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. What is a tiling?
Tilings or tessellations are coverings of the plane with tiles.
Tessellations are made with basic shapes made from triangles, rectangles, pentagons, or hexagons (couldn’t find a cool picture of a pentagon) Buckyball is a fairly new chemical with a 3-D structure formed by connecting carbon molecules with pentagon shapes and carbon molecules hexagon shapes together.

11. Most Famous: Escher
Escher was the most famous artist with respect to tessellations
Escher started reading his father’s calculus books when he was a young boy. He assumed that is was simply a language that he did not yet learn but was fascinated by the relationship between mathematics and art.
“To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of art.” ~M.C. Escher

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)