# Difference between revisions of "Non-Euclidean Art Project"

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{{Project}} | {{Project}} | ||

− | The project consists of two parts: a project and a paper. | + | The project consists of two parts: a project and a paper. They are each worth 50 points. |

− | Choose either spherical or hyperbolic geometry - don’t do both! | + | Choose either the spherical geometry or hyperbolic geometry project - don’t do both! |

==Spherical Geometry Project== | ==Spherical Geometry Project== | ||

Create an art project involving Spherical Geometry. | Create an art project involving Spherical Geometry. | ||

+ | |||

Some ideas: | Some ideas: | ||

− | + | * Make a spherical tessellation. | |

− | + | * Take one of Escher's spherical Tessellations and modify it. | |

− | + | * Write a poem/short story involving Spherical Geometry. | |

+ | |||

Be creative! Find a way to apply what you know about the topics mentioned above. | Be creative! Find a way to apply what you know about the topics mentioned above. | ||

+ | |||

+ | |||

Write a paper about Spherical geometry. | Write a paper about Spherical geometry. | ||

+ | |||

The paper should be a minimum of 3 pages, typed, double-spaced, 1 inch margins. Figures are excluded from the page count. | The paper should be a minimum of 3 pages, typed, double-spaced, 1 inch margins. Figures are excluded from the page count. | ||

− | + | * Explain how this geometry is different from Euclidean geometry. How are the axioms different? What polygons exist? Which ones do not exist? | |

− | + | * What do we know about the theory of tessellations on the sphere? How many regular tessellations are there? Do you think all triangles tessellate? Do all quadrilaterals tessellate? | |

− | + | * What do the isometries of the sphere look like? | |

==Hyperbolic Geometry Project== | ==Hyperbolic Geometry Project== | ||

Create an art project involving Hyperbolic Geometry. | Create an art project involving Hyperbolic Geometry. | ||

+ | |||

Some ideas: | Some ideas: | ||

− | + | * Make an interesting hyperbolic tessellation (more intricate than basic triangles). | |

− | + | * Take a simple hyperbolic tessellation and turn it into an Escher like tessellation by decorating it. | |

− | + | * Take one of Escher's hyperbolic tessellations and modify it. | |

− | + | * Write a poem or short story involving Hyperbolic geometry. | |

+ | |||

Be creative! Find a way to apply what you know about the topics mentioned above. | Be creative! Find a way to apply what you know about the topics mentioned above. | ||

+ | |||

+ | |||

Write a paper about Hyperbolic geometry. | Write a paper about Hyperbolic geometry. | ||

+ | |||

The paper should be a minimum of 3 pages, typed, double-spaced, 1 inch margins. Figures are excluded from the page count. | |||

− | + | * Explain how this geometry is different from Euclidean geometry. How are the axioms different? What polygons exist? Which ones do not exist? | |

− | + | * What do we know about the theory of tessellations on hyperbolic space? How many regular tessellations are there? Do you think all triangles tessellate? Do all quadrilaterals tessellate? | |

− | + | * What do the isometries of the hyperbolic plane look like? |

## Revision as of 11:20, 25 April 2007

The project consists of two parts: a project and a paper. They are each worth 50 points.

Choose either the spherical geometry or hyperbolic geometry project - don’t do both!

## Spherical Geometry Project

Create an art project involving Spherical Geometry.

Some ideas:

- Make a spherical tessellation.
- Take one of Escher's spherical Tessellations and modify it.
- Write a poem/short story involving Spherical Geometry.

Be creative! Find a way to apply what you know about the topics mentioned above.

Write a paper about Spherical geometry.

- Explain how this geometry is different from Euclidean geometry. How are the axioms different? What polygons exist? Which ones do not exist?
- What do we know about the theory of tessellations on the sphere? How many regular tessellations are there? Do you think all triangles tessellate? Do all quadrilaterals tessellate?
- What do the isometries of the sphere look like?

## Hyperbolic Geometry Project

Create an art project involving Hyperbolic Geometry.

Some ideas:

- Make an interesting hyperbolic tessellation (more intricate than basic triangles).
- Take a simple hyperbolic tessellation and turn it into an Escher like tessellation by decorating it.
- Take one of Escher's hyperbolic tessellations and modify it.
- Write a poem or short story involving Hyperbolic geometry.

Be creative! Find a way to apply what you know about the topics mentioned above.

Write a paper about Hyperbolic geometry.

- Explain how this geometry is different from Euclidean geometry. How are the axioms different? What polygons exist? Which ones do not exist?
- What do we know about the theory of tessellations on hyperbolic space? How many regular tessellations are there? Do you think all triangles tessellate? Do all quadrilaterals tessellate?
- What do the isometries of the hyperbolic plane look like?