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 --- --- Spherical 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?)