Sample Course Outline

From EscherMath

THIS PAGE SHOULD BE DELETED AS THERE ARE NOW COURSE OUTLINES FROM COURSES TAUGHT USING THIS WIKI

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.

Contents 1 Week 1 - Euclidean Geometry 2 Week 2 - Symmetry 3 Week 3 - Basic Tessellations 4 Week 4- More Tessellations 5 Week 5 - Escher’s tessellation 6 Week 6 - Border Patterns, Wallpaper Groups 7 Week 7 - Basilica visit and Project 1 8 Week 8 - Exam 9 Week 9 - Spherical Geometry 10 Week 10 - Hyperbolic Geometry 11 Week 11 - Non-Euclidean Geometry 12 Week 12 - Fractals 13 Week 13 - Fractals, 2 and 3 dimensions 14 Week 14 - The 4th dimension 15 Week 15 - The 4th dimension

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.
• Homework 1

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
• Polyominoes 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.
• Do Flatland Exploration

Week 15 - The 4th dimension

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