Comparison between the three geometries Exploration
From EscherMath
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?) | |||
| 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?) |
