The Art of Tessellations

Introduction

Welcome to the world of tessellations! On this amazing journey into the art of tessellations, you will identify many of the transformations and symmetries found encircling you. You will find shapes in art, nature and everyday life. Think translations, rotations, and reflections! They are everywhere!

Your task as you explore tessellations is to consider the following questions: Who is considered responsible for tessellations? Which polygons tessellate? What is the sum of each vertex? Where are you most likely to find tessellations? And many more…

Click the "TASK" button to begin your journey...

Task

Tessellations? You mean those repeating pattern of figures that cover a plane without gaps or overlaps?

Your goal as you meander your way through this webquest is:

to learn more about the history of tessellations
to explore what tessellations are along with some interesting facts
to decide which polygons “qualify” as tessellations
to investigate where tessellations may be in your surroundings (food, animals, buildings, etc.)
to create a tessellation yourself

READY? SET ? then CLICK on "Process" to continue.

Process

Let the fun begin!

Here is a little history behind tessellations:

Maurits Cornelis Escher, born in Leeuwarden, Holland in 1898, created unique and fascinating works of art that explore and exhibit an array of mathematical ideas. Among his greatest admirers were mathematicians, who recognized in Escher’s work an extraordinary visualization of mathematical principles. This was quite remarkable as Escher had no formal mathematics training beyond secondary school.

Interesting! Next let's make sure we are all on the same thought pattern before proceeding. Check out this website to review:

http://www.mathsisfun.com/geometry/tessellation.html

Now take this quiz…

http://www.nelson.com/mathfocus/grade8/quizzes/ch07/mf8_ch.7_lesson_2try.htm

How did you do? You may take it again if you would like. Thanks!

Your journey continues through the art of tessellations with you creating your own computer-generated tessellation. Click on this link:

http://illuminations.nctm.org/Activity.aspx?id=3533

and remember to utilize the links at the top of this website to manuever the site to its fullest potential. Spend at least 10 minutes but no more than 15 minutes on this activity before moving on to your next activity.

Time to create your own tessellation using paper, scissors, tape, colored markers/pencils, and your imagination. Here are step-by-step steps to assist you.

http://www.tessellations.org/methods-diy-papercut.shtml

Please collect your supplies from the supply table and get started. You will be evaluated using the rubric found under the "Evaluation" heading.

Evaluation

What have you learned? Be prepared to answer these questions and others during our class discussion.

Which of the shapes tessellate by themselves? Can you cover the plane with just triangles? just squares? just pentagons?
Try to find a way to make a tessellation with just squares and octagons. Which other combinations of shapes tessellate?
Is there a way to tell if shapes will tessellate by looking at the properties of those shapes? How?

Hint: The length of the sides of all the shapes are all the same. Only the angles are different. What are the angles in each shape?

Here is the rubric which will be used to evaluate your tessellation:

TESSELLATION RUBRIC

CATEGORY	4	3	2	1
Organization	Tessellations are presented in an organized manner. Their construction is complete and accurate.	Tessellations are presented in a somewhat organized manner. Their construction is fairly complete.	Tessellations are organized, but not well constructed.	There is no organization to the tessellation.
Complexity of Design	Tessellation was created with non- polygon shapes that connect to create an intricate and complex pattern.	Tessellation was created with complex polygon shapes that connect to create an intricate and complex pattern.	Tessellation was created with simple shapes that connect to create a pattern	Tessellation is simple and pattern is not complex or interesting.
Completeness of Tessellation	All areas of the tessellation are covered by the complex pattern to completely fit together.	All areas of the tessellation are covered by the simple pattern with few or small holes in the pattern.	Most areas of the tessellation are covered by the simple pattern with some holes in the pattern.	There are major holes in the tessellation and it does not fit together.
Creativity	Tessellation uses unique design and patterns of unusual shapes to form a complex and interesting design.	Tessellation uses a mixture of polygons and interesting shapes to create a nice design.	Tessellation uses some shapes that fit together to form a simple pattern	There is no creativity to the design.
Follows Directions	Tessellation covers an 8.5"x11" sheet of paper completely with interesting display and presentation.	Tessellation covers an 8.5"x11" sheet of paper and has a complete presentation.	Tessellation mostly covers an 8.5"x11" sheet of paper and has no presentation	Tessellation does not cover the 8.5"x11" paper completely.

Maximum of 20 pts. earned here

Conclusion

Now you have completed your tessellation project and learned about Maurits Cornelis Escher, the father of tessellations. Be sure to take time to look around and be aware of tessellations that surround you whether it is on the floor (rugs, tiles, etc.), in your food (pineapple, kiwi, etc.), or in the architecture of buildings in your community. Happy tessellation hunting!

Bruce Bilney's Escher-style tessellation art, seahorse theme