Difference between revisions of "Comparison between the three geometries Exploration"
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! Semi-regular tessellations. | ! Semi-regular tessellations. | ||
(How many different ones are there?) | (How many different ones are there?) | ||
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! Isometries | ! Isometries | ||
(Which ones have we encountered?) | (Which ones have we encountered?) | ||
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! Area of a triangle. | ! Area of a triangle. | ||
(What is the formula?) | (What is the formula?) | ||
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! Escher’s work based on each geometry. | ! Escher’s work based on each geometry. | ||
(How extensively did he work on each of the geometries?) | (How extensively did he work on each of the geometries?) | ||
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Revision as of 11:20, 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?) |
