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Activity 2: Graphic Design: Using Symmetry to Create Corporate Logos (Grade Level 68)

The Geometry of Bicycle Designs | Using Symmetry to Create Corporate Logos | Patterns and Weaving | Career Connections | More Math Concepts

Standards:

Standard 3: Geometry and Spatial Sense (Transformations and Symmetry)

* These standards have been adopted and are based on the information from Principals and Standards for School Mathematics: Discussion Draft, October l998, National Council of Teachers of Mathematics.

Objectives:

  • Describe three types of symmetry
  • Categorize symmetric figures based on type of symmetry
  • Create figures using different type of symmetry

adobe acrobat Student Activity (PDF File)
Answers (PDF File)

Activity 2

Three simple types of symmetry are reflection, rotation, and translation. In each case, we start with an original image and, using symmetry, we can transform it.

Reflection symmetry is sometimes called "mirror" or "flip" symmetry. It's easy to see why. A butterfly (see below) may have reflection symmetry because one side is a mirror image of the other.

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Notice that a vertical line down the center of the butterfly's body serves as what is called the "line of symmetry."

The letter A has reflection symmetry similar to the butterfly.

symmetry

1. Look at the letters of our alphabet below. Organize the letters according to which ones have reflection symmetry into three groups: the letters that have reflection symmetry with a vertical line of symmetry (like the letter A), those with a horizontal line of symmetry, and those with both vertical and horizontal lines of symmetry.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

symmetry

A second type of symmetry is called rotation symmetry. You produce rotation symmetry by turning an object. By rotating the flag on the left 90 degrees, we produce a new flag.

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The third type of symmetry is translation symmetry. It is produced by moving the object forward, backwards, or in any direction but do not flip or turn it. The heart shape below (which has reflection symmetry) was translated to three other shapes (or positions).

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2. A graphic artist uses symmetry to create designs that become the symbol for companies. These are called corporate logos. Look at the nine examples below (a-i). Can you tell which ones have reflection, rotation, or translation symmetry? For each logo, describe the symmetry you find and how symmetry might have been used to create the logo.

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a b c
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d e f
symmetry symmetry symmetry
g h i

3. Design your own logo. Notice that many logos start with a basic shape, a rectangle, a diamond, or an oval, and then the artist uses symmetry to create the design. The Mitsubishi company logo below began with a diamond that was rotated 120 degrees, then another 120 degrees from that.

symmetry

a. Pick a basic shape from among those below.

b. Cut out at least three copies and use reflection, rotation, or translation symmetry to create your own logo.

c. Write a description in your own words of the type or type of symmetry you used to create your logo.

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The final figure was achieved by a combination of refection and rotation. One original triangle was first placed on the page, an identical copy was reflected horizontally. Two triangles were rotated 90 degrees. One left in place, the other reflected vertically. The base of each triangle was superposed, then the rotated group was superimposed over the center of the base of the other pair.

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Students should be encouraged to use color to enhance their designs:

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symmetry