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.


Comparing and Contrasting the 3 geometries
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?)