# Difference between revisions of "Sample Course Outline"

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+ | <b>THIS PAGE SHOULD BE DELETED AS THERE ARE NOW COURSE OUTLINES FROM COURSES TAUGHT USING THIS WIKI</b> | ||

− | This is just one of many possible course outlines | + | 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. | ||

==Week 1 - Euclidean Geometry == | ==Week 1 - Euclidean Geometry == | ||

− | Read the | + | * 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 == | == Week 2 - Symmetry == | ||

− | Read section | + | |

− | Read Schattschneider page 1-19 | + | Learn more about symmetry with: |

+ | *[[Symmetric Figures Exploration]] | ||

+ | *[[Symmetry of Stars and Polygons Exploration]] | ||

+ | *[[Symmetry and Celtic Knots Exploration]] | ||

+ | |||

+ | * Read section [[Introduction to Symmetry]] | ||

+ | * Read Schattschneider page 1-19 | ||

== Week 3 - Basic Tessellations == | == Week 3 - Basic Tessellations == | ||

− | Labor Day Holiday - day off | + | * Labor Day Holiday - day off |

− | Read Schattschneider page 19-34 | + | * Read Schattschneider page 19-34 |

+ | * [[Tessellation Exploration: The Basics]] | ||

+ | * [[Tessellations: Why There Are Only Three Regular Tessellations]] | ||

== Week 4- More Tessellations == | == Week 4- More Tessellations == | ||

− | Read Schattschneider page 34-52 | + | * Read Schattschneider page 34-52 |

+ | * Read [[Tessellations by Polygons]] | ||

+ | * [[Polyominoes Exploration]] | ||

== Week 5 - Escher’s tessellation == | == Week 5 - Escher’s tessellation == | ||

− | Read | + | * 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 == | == Week 6 - Border Patterns, Wallpaper Groups == | ||

− | Read section about Border Patterns | + | * 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 == | == Week 7 - Basilica visit and Project 1 == | ||

− | Work on proposals for the Project. Have students brain storm in class. | + | * 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. | + | * Discuss the fieldtrip to the Basilica Cathedral. See [[Seeking Symmetry]] |

== Week 8 - Exam == | == Week 8 - Exam == | ||

− | Fall Break | + | * Fall Break |

− | Exam 1 | + | * Exam 1 |

== Week 9 - Spherical Geometry == | == Week 9 - Spherical Geometry == | ||

− | 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]]. |

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

− | Read the section on [[Spherical Geometry]] | + | * Start working on homework assignment in class. |

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

== Week 10 - Hyperbolic Geometry == | == Week 10 - Hyperbolic Geometry == | ||

− | Read the section on [[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 == | == 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 == | == Week 12 - Fractals == | ||

− | Exam 2 | + | * Read [[Similarity Transformations]] |

+ | * Do [[Self-Similarity : A first look]] | ||

+ | * Do [[Self-Similarity Exploration]] | ||

+ | * Exam 2 | ||

== Week 13 - Fractals, 2 and 3 dimensions == | == 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 == | == Week 14 - The 4th dimension == | ||

− | Thanksgiving Holiday - Days off | + | * Thanksgiving Holiday - Days off |

− | + | * Read [[The Fourth Dimension]] | |

+ | * Read Flatland : | ||

+ | ** [http://www.alcyone.com/max/lit/flatland/ Flatland] or | ||

+ | ** [http://www.geom.uiuc.edu/~banchoff/Flatland/ Flatland] This site includes copies of the illustrations. | ||

+ | * Do [[Flatland Exploration]] | ||

== Week 15 - The 4th dimension == | == Week 15 - The 4th dimension == | ||

+ | * Read [http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein |

## Latest revision as of 23:51, 28 August 2014

**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
- Symmetry and Celtic Knots 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:

## 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 :
- Do Flatland Exploration

## Week 15 - The 4th dimension

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