Difference between revisions of "Comparison between the three geometries Exploration"
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|+ Comparing and Contrasting the 3 geometries | |+ Comparing and Contrasting the 3 geometries | ||
| − | ! Question !! | + | ! Question !! --- Euclidean Geometry --- !! --- Sperical Geometry --- !! --- Hyperbolic Geometry --- |
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! Geodesics | ! Geodesics | ||
Revision as of 11:23, 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?) |
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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?) |
|||
| 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?) |
