1. Tessellations

2. A tessellation is any repeating pattern of interlocking shapes.
What is a Tessellation?
A tessellation is any repeating pattern of interlocking shapes.
The word tessellation comes from the Latin Tessella, which was a small Square stone or tile used in ancient Roman mosaics.  Tiles and Mosaics are common synonyms for tessellations. 
Some shapes, or polygons, will tessellate and others will not.  As for the regular polygons, tessellations can easily be created using squares, equilateral triangles and hexagons.

3. Tessellations can be simple…

4. Tessellations can also be very complex…

5. M.C. Escher
Maurits Cornelis (M.C.) Escher ( ) is one of the world's most famous graphic artists.
During his lifetime, Escher made 448 lithographs, woodcuts and wood engravings and over 2000 drawings and sketches Apart from being a graphic artist, Escher illustrated books, designed tapestries, postage stamps and murals .
Using a mathematical technique called "tessellation," Escher produced complex patterns based on repeating shapes in the forms of butterflies and fish, birds, and lizards..

6. Escher used the geometry in his art that he saw at Alhambra
* As his work developed, he drew great inspiration from mathematical ideas he read about, often working directly from geometric shapes.
* He was also fascinated with paradox and "impossible" figures, and developed many intriguing works of art.

7. Convex Concave Lithograph, March 1955

8. Escher was fascinated by every kind of tessellation
In 1957 he wrote an essay on tessellations. Escher used these basic shapes in his tessellations.
triangle, square, and hexagon

9. Sometimes Escher changed the basic shapes
By “distorting” the basic shapes he changed them into animals, birds, and other figures.
The effect can be
both startling and beautiful.

10. How might Escher have created a tessellation such as the one below

11. How might Escher have created a tessellation such as the one below
Using patty paper trace the base shape and investigate what transformations were used to create the Pegasus tessellation.
Record your findings being as descriptive as possible.

12. How might Escher have created a tessellation such as the one below
Using patty paper trace the base shape and investigate what transformations were used to create the Dog tessellation.
Record your findings being as descriptive as possible.

13. How might Escher have created a tessellation such as the one below
Using patty paper trace the base shape and investigate what transformations were used to create the Lizzard tessellation.
Record your findings being as descriptive as possible.

14. How might Escher create a tessellation such as the one below
Go to the website
Enter the code: ZNKV8
Here you will find 3 interactive worksheets for you to investigate the Escher Tessellations further.