1. The art of M.C. Escher and tessellations Circle Limit III, 1959

2. Definitions we need to know:  1. Vertex:  A: a point (as of an angle, polygon, polyhedron, graph, or network) that terminates a line or curve or comprises the intersection of two or more lines or curves 2. Angle: A: the space within two lines or three or more planes diverging from a common point, or within two planes diverging from a common line

3. 3. Plane: A:Geometry, a surface generated by a straight line moving at a constant velocity with respect to a fixed point. B: Fine Arts, an area of a two-dimensional surface having determinate extension and spatial direction or position: oblique plane; horizontal plane 4. Polygon: A: a closed plane figure bounded by straight lines B: a closed figure on a sphere bounded by arcs of great circles

4. 5. Adjacent: A: Having a common endpoint or border (adjacent lots) (adjacent sides of a triangle) 6. Congruent: A: Geometry, coinciding at all points when superimposed, congruent triangles

5. What is a tessellation? The dictionary defines a tessellation as: A: Mosaic B: a covering of an infinite geometric plane without gaps or overlaps by congruent plane figures of one type or a few types

6. A tessellation has three main properties: 1.They are repeated patterns, but they are a specific kind of repeated pattern. 2. Tessellations do not have gaps or overlaps. 3. Tessellations can continue on a plane forever.

7. The history of tessellations goes back to Sumeria in about 4000 BC. The Sumerians built their homes and temples using mosaic tiles decorated with geometric patterns. Throughout history, many civilizations such as the Persians, Moors and Romans used these decorative tiles extensively. The English word tessellation comes from the Roman word for tile: tessellae. This is an Islamic roof tessellation from Chehel Sotoon, 1642-1667. Islamic religion forbids the use of anything living in their art so mosaics using complex shapes and patterns were used quite frequently.

8. Pat Wehrman is a tile artist that is also an engineer. She is heavily influenced by M. C. Escher and creates mosaic’s with tiles using tessellations.

9. M.C. Escher was born in the Netherlands in 1898. He became one of the most famous graphic designers in the world. He did many realistic drawings and prints as well but he is very famous for his mathematical tessellations, many of which are extremely complex. Just like Leonardo da Vinci and Michelangelo, Escher was left handed. Escher passed away in 1972 but during his lifetime he created 448 lithographs, woodcuts and wood engravings and over 2000 drawings and sketches. He is still a very talked about artist today, not just for his art but for the mathematics behind it!

10. Lithograph, 1921 Symmetry series, 1936-1941

12. We are going to begin cutting a shape to make our own tessellation pieces from the 2 ½” X 2 ½” cardstock pieces I have provided. Although each person’s template will be a different shape, we will all end up with a template similar to this

13. I turned my template into a dog. What will yours be?

14. We will be going from this……to this!