M.C. Escher and Hyperbolic Geometry

Math Explorer Club


The Dutch artist M. C. Escher is known for his repeating patterns of interlocking motifs, tessellations of the Euclidean and the hyperbolic plane and his drawing representing impossible figures.

Without having any mathematical knowledge, he managed to represent many mathematical concepts belonging to non-Euclidean geometry and many of his drawings are used by mathematicians to illustrate examples.

We will present here both his work and the mathematics behind it.

M.C. Escher
1929 Lithograph


  1. Introduction: M.C. Escher, short biography

  2. Escher's Work: Spatial structure, flat surface structure and the relationship between them

  3. The approach to infinity

  4. Euclidean and non-Euclidean geometry

  5. Hyperbolic geometry

  6. The complex half-plane model for the hyperbolic plane

  7. The Poincaré model for the hyperbolic plane

  8. Escher's Tessellations of the plane

  9. Tessellations of the Euclidean and non-Euclidean plane

  10. References

This work was made possible due to a grant from the National Science Foundation.