tessellations this presentation is based on the work of melissa hogg and miranda hodge
TRANSCRIPT
![Page 1: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/1.jpg)
Tessellations
This presentation is based on the work of Melissa Hogg and Miranda
Hodge
![Page 2: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/2.jpg)
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.
![Page 3: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/3.jpg)
Tessellations Around Us
• Tessellations are everywhere.
• How many tessellations have you seen today?
![Page 4: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/4.jpg)
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?
![Page 5: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/5.jpg)
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.
![Page 6: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/6.jpg)
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
![Page 7: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/7.jpg)
Regular Tessellations
• Uses only one type of regular polygon • Rules:
1. the tessellation must tile an infinite floor without gaps or overlapping2. the tiles must all be the same regular polygon3. each vertex must look the same.
![Page 8: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/8.jpg)
Regular Tessellations: Examples
![Page 9: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/9.jpg)
Semi-regular Tessellations
• Uniform tessellations that contain two or more regular polygons
• Same rules apply
![Page 10: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/10.jpg)
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.
![Page 11: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/11.jpg)
Tessellation Nomenclature Examples
![Page 12: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/12.jpg)
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
![Page 13: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/13.jpg)
M. C. Escher
![Page 14: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/14.jpg)
M. C. Escher
![Page 15: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/15.jpg)
Escher, again
![Page 16: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/16.jpg)
![Page 17: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/17.jpg)
![Page 18: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/18.jpg)
![Page 19: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/19.jpg)
Transformations with Tessellations
![Page 20: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/20.jpg)
Student Examples
![Page 21: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/21.jpg)
Student Examples
![Page 22: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/22.jpg)
Student Examples
![Page 23: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/23.jpg)
Student Examples
![Page 24: Tessellations This presentation is based on the work of Melissa Hogg and Miranda Hodge](https://reader036.vdocuments.site/reader036/viewer/2022081420/5697bf7c1a28abf838c840ea/html5/thumbnails/24.jpg)
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.htmlModern Day Artists Inspired my MC Escher
www.geocities.com/davidschow/HUB/Esample.htm
Michael Saiki Grade 5 Rico Boja Grade 2