1. Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge

2. What Is a Tessellation? A shape or tile that repeats to fill a surface without any gaps or overlaps. The name comes from the word tessella, the small square tile used in ancient Roman mosaics.

3. Tessellations Around Us Tessellations are everywhere. How many tessellations have you seen today?

4. Geometry & Tessellations Many different geometric shapes can be used to create tessellations. Which of the shapes below would fit with itself to make a good tessellation design?

5. Patterns Very basic tessellations are simply a repeating pattern. The rule is that you have to make sure that the shapes fit together leaving no open space on the page.

6. Symmetry Symmetry is an important part of tessellations. Geometric shapes can be translated, reflected, and rotated. These moves, alone or combined, can create interesting tessellation designs. Translation Rotation Reflection

7. Regular Tessellations Uses only one type of regular polygon Rules: 1. the tessellation must tile an infinite floor without gaps or overlapping 2. the tiles must all be the same regular polygon 3. each vertex must look the same.

8. Regular Tessellations: Examples

9. Semi-regular Tessellations Uniform tessellations that contain two or more regular polygons Same rules apply

10. Tessellation Nomenclature A tessellation of squares is named "4.4.4.4". Here's how: choose a vertex, and then count the number of sides each polygon has that forms the vertex.

11. Tessellation Nomenclature Examples

12. Professional Tessellation Designs Many artists have created master works of art based on tessellations. M.C. Escher (“The Father of Tessellations”) and Robert Ingalls are two of the most famous. Sun and Moon M.C. Escher Fish Robert Ingalls

13. M. C. Escher

15. Escher, again

19. Transformations with Tessellations

20. Student Examples

24. References Beyer, Jinny. Designing Tessellations. Chicago: Contemporary Books, 1999. Britton, Jill. Escher in the Classroom. http://ccins.camosun.bs.ca/~jbritton/jbescher.htm Math Forum mathforum.org/sum95/suzanne/tess.intro.html Modern Day Artists Inspired my MC Escher www.geocities.com/davidschow/HUB/Esample.htm Michael Saiki Grade 5Rico Boja Grade 2