# Difference between revisions of "Sample Course Outline"

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* Do the [[Spherical Geometry Exploration]] to introduce the main ideas from 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]]. | * Another approach to an introduction is the [[Spherical Easel Exploration]]. | ||

+ | * Explore spherical geometry using the [[Spherical Easel Exploration]] | ||

* Further exploration: [[Spherical Geometry: Polygons]] | * Further exploration: [[Spherical Geometry: Polygons]] | ||

* Read the section on [[Spherical Geometry]] | * Read the section on [[Spherical Geometry]] |

## Revision as of 10:25, 24 July 2007

This is just one of many possible course outlines. The course outlined below was taught in 2004. This course met three times a week 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.

## 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:

## 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.
- Explore spherical geometry using the Spherical Easel Exploration
- Further exploration: Spherical Geometry: Polygons
- Read the section on Spherical Geometry

## Week 10 - Hyperbolic Geometry

Read the section on Hyperbolic Geometry

## Week 11 - Non-Euclidean Geometry

Reader: 134-146

## Week 12 - Fractals

Exam 2

## Week 13 - Fractals, 2 and 3 dimensions

## Week 14 - The 4th dimension

Thanksgiving Holiday - Days off