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.
+
Make a spherical tessellation.
Take one of Escher's spherical Tessellations and modify it.
+
Take one of Escher's spherical Tessellations and modify it.
Write a poem/short story involving Spherical Geometry.
+
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?
+
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 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?
+
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).
+
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 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.
+
Take one of Escher's hyperbolic tessellations and modify it.
Write a poem or short story involving Hyperbolic geometry.
+
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.
 
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?
+
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 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?
+
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.

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?