Non-Euclidean Art Project

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The project consists of two parts: a project and a paper.

Choose either spherical or hyperbolic geometry - 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?