
Escher tried to illustrate the concept of infinity in
several works. On the left, he uses what is mathematically known as the
"Poincare"disk to tile a twodimension object with a geometry different from the
standard Euclidian one. Notice how
there is again a certain symmetry, involving "curved squares" and "curved
triangles", but they are no longer all of the same size.
Toward the edge of the circle, the fish are getting
smaller and smaller, and they accumulate near the boundary.
Mathematically, the boundary of the (Poincare) disk has
infinite circumference, when measured according to the Poincare distance. 