Comparison between the three geometries Exploration
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Objective: Compare and contrast Eclidean, spherical and hyperbolic geometry
Fill in the following table with as much detail as you can.
| Question | --- Euclidean Geometry --- | --- Spherical Geometry --- | --- Hyperbolic Geometry --- |
|---|---|---|---|
| Geodesics
(What do they look like?) |
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| Parallel Lines
(How many, if any?) |
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| Polygons (Do we get new ones?
Which ones don’t exist?) |
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| Sum of the angles in a triangle. | |||
| Regular tessellations
(How many different ones are there?) |
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| Semi-regular tessellations.
(How many different ones are there?)
|
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| Isometries
(Which ones have we encountered?) |
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| Area of a triangle.
(What is the formula?) |
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| Escher’s work based on each geometry.
(How extensively did he work on each of the geometries?) |
