Sample Course Outline

This is just one of many possible course outlines.

A course very much like the one outlined below was taught in 2004.

This course met three times a week (50 minute sessions) for 15 weeks.

This section is unfinished.

Week 1 - Euclidean Geometry

• Do the Quadrilaterals Exploration
• Do the Triangles and Quadrilaterals Exploration
• Do the Tessellations, a first look Exploration
• Read the Fundamental Concepts with special attention to triangles, quadrilaterals and convexity.

Week 2 - Symmetry

Learn more about symmetry with:

• Symmetric Figures Exploration
• Symmetry of Stars and Polygons Exploration
• Rotational and Reflectional Symmetry in Escher’s Prints
• Celtic Art Exploration

• Read section Introduction to Symmetry
• Read Schattschneider page 1-19

Week 3 - Basic Tessellations

• Labor Day Holiday - day off
• Read Schattschneider page 19-34
• Tessellation Exploration: The Basics
• Tessellations: Why There Are Only Three Regular Tessellations

Week 4- More Tessellations

• Read Schattschneider page 34-52
• Read Tessellations by Polygons
• Polynominoes Exploration

Week 5 - Escher’s tessellation

• Read Tessellations by Recognizable Figures
• Do Wallpaper Exploration
• Do Escher-Like Tessellations Explorations
• Look at Escher Tessellations Using Geometer’s Sketchpad

Week 6 - Border Patterns, Wallpaper Groups

• Read section about Border Patterns (also known as Frieze Patterns )

Possible explorations:

• Frieze Names Exploration
• Identifying Border Patterns Exploration

Week 7 - Basilica visit and Project 1

• Work on proposals for the Project. Have students brain storm in class. See Tessellation Art Project for details.
• Discuss the fieldtrip to the Basilica Cathedral. See Seeking Symmetry

Week 8 - Exam

• Fall Break
• Exam 1

Week 9 - Spherical Geometry

• Do the Spherical Geometry Exploration to introduce the main ideas from Spherical Geometry.
• Another approach to an introduction is the Spherical Easel Exploration.
• Further exploration: Spherical Geometry: Polygons
• Start working on homework assignment in class.
• Read the section on Spherical Geometry

Week 10 - Hyperbolic Geometry

• Intro to Hyperblic Geometry using Escher's Circle Limit Exploration
• Do Ideal Hyperbolic Tessellations Exploration
• Another possibility is Hyperbolic Geometry Exploration
• Read the section on Hyperbolic Geometry

Week 11 - Non-Euclidean Geometry

• Hyperbolic Geometry with Noneuclid II Exploration
• Comparison between the three geometries Exploration
• Start working on homework assignment in class.
• Read The Three Geometries

Week 12 - Fractals

• Read Similarity Transformations
• Do Self-Similarity : A first look
• Do Self-Similarity Exploration
• Exam 2

Week 13 - Fractals, 2 and 3 dimensions

• Read Fractals
• Do Escher Fractal Exploration
• Do Fractal Dimension Exploration
• Do [[Escher's Impossible Figures on the Internet Exploration)

Week 14 - The 4th dimension

• Thanksgiving Holiday - Days off
• Read The Fourth Dimension
• Read Flatland :
  • Flatland or
  • Flatland This site includes copies of the illustrations.

Week 15 - The 4th dimension

• Read And he built a crooked house… , Short story by Robert A. Heinlein