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

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.

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

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.

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?