Nonlinear Tessellations

Background

To prepare for studying tessellations of the hyperbolic plane, we survey some of Escher's work.

Next we see some of Escher's attempts to represent the infinite.

A word about tessellations, regular divisions of the plane into congruent figures.

What makes some geometries Non-Euclidean?

To study hyperbolic geometry we use the Poincare disc.

Here are some basic circle inversion constructions we shall use.

Here are the concepts from hyperbolic geometry that we shall use.

To prepare for studying tessellations of the hyperbolic plane, we survey some of Escher's work.
Next we see some of Escher's attempts to represent the infinite.
A word about tessellations, regular divisions of the plane into congruent figures.
What makes some geometries Non-Euclidean?
To study hyperbolic geometry we use the Poincare disc.
Here are some basic circle inversion constructions we shall use.
Here are the concepts from hyperbolic geometry that we shall use.