# Difference between revisions of "Comparison between the three geometries Exploration"

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! Polygons (Do we get new ones? | ! Polygons (Do we get new ones? | ||

Which ones don’t exist?) | Which ones don’t exist?) | ||

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## Revision as of 11:19, 24 July 2007

**Objective:**
Compare and contrast Eclidean, spherical and hyperbolic geometry

Fill in the following table with as much detail as you can.

Question | Euclidean Geometry | Sperical Geometry | Hyperbolic Geometry | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Geodesics
(What do they look like?) |
|||||||||||||||||||||||||||

Parallel Lines
(How many, if any?) |
Polygons (Do we get new ones?
Which ones don’t exist?) |
Sum of the angles in a triangle. | Regular tessellations
(How many different ones are there?) |
Semi-regular tessellations.
(How many different ones are there?) |
Isometries
(Which ones have we encountered?) |
Area of a triangle.
(What is the formula?) |
Escher’s work based on each geometry.
(How extensively did he work on each of the geometries?) |