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Chapter 9

Transformations and Design

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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

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The Big Picture

Design a business Create a logo (applying principles

from chapter) Design a product for your business

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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)

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Activity 1: The VVWA

Verbal and Visual Word Association is a reading strategy for learning new vocabulary terms

Word Visual

Verbal = definition Personal

Association

Website: http://www.intermath-uga.gatech.edu/dictnary/homepg.asp

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Using Dynamic Geometry Software

Geometer sketchpad

Winplot (http://math.exeter.edu/rparris/winplot.html)

Simple graphing program: http://www.serpik.com/agrapher/

Autograph

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Designing a Logo

Points to rememberKeep it clean and simple

FontThick = strength and power

Script = elegance

Slant = movement

ColourBlue, maroon, dark teal = conservative

Black and white = contemporary

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Designing a Logo

Software cites to look at:Logo design software: http://www.aaa-logo.com

Microsoft Photodraw

CorelDraw (http://www.corel.com)

Adobe Illustrator and Adobe Photoshop (http://www.adobe.com/support/downloads)

Macromedia Freehand or Flash (http://www.macromedia.com/downloads/)

Drawing program: http://www.drawinghand.com/

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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.

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What is a tiling?

Tilings or tessellations are coverings of the plane with tiles.

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Most Famous: Escher

““To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of art.”To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of art.”~M.C. Escher~M.C. Escher

Escher was the most famous artist with respect to tessellations

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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)