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{{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?