- Go to www.google.com and enter
"totally tessellated" for your google search topic. Press "I'm
Feeling Lucky" and you should go to the "Totally
Tessellated" website. Or, you can go there directly by entering:
- Click on "click here to view this site" or the image of the site
to end up on the Welcome Page. Read the Welcome Page.
- This website is an excellent resource for learning about tessellations.
It is an extremely large site and has several topics and subtopics to browse
through. To help you navigate through the "Totally
Tessellated" website, I have provided a map on the last page. If
you ever get lost or stuck just quit the site and restart from step 1 above.
Part 2 - Research the Essentials
- Go to the first section, "Background," and read/look through the
various pages. Sketch an example of the following translations:
- Go to the "Regular Tessellation" page of the second section, "Simple
Tessellations with Regular Polygons."
a) Write the definition of a regular polygon.
b) Which regular polygons tessellate the plane?
c) What qualities do all the regular polygons that tessellate share in common?
- Go to the "Semi - Regular Tessellation" page under the second
a) Sketch two examples of tessellations with more than
one regular polygon.
- Go to the third section, "Simple Tessellations of Non-regular Polygons,"
and look at both categories ("Triangles" and "Quadrilaterals").
a) Sketch one example of a non-regular triangle tessellation.
b) Sketch one example of a non-regular quadrilateral tessellation.
Part 3 - Research Escher
- Click "Escher on the top menu bar and you should end up on an Introduction
page. Read this.
- Next Click on "Biography" on the right side of your screen. There
are three pages in the biography section ("Introduction," "Timeline,"
"Relationship to Mathematics"). Visit all three pages to answer
the following questions.
a) When and where was M.C. Escher born?
b) When and where did M.C. Escher die?
c) What does "M.C." stand for?
d)Escher visited an Islamic temple that inspired him to begin working with
tessellations. Where was this temple located?
e) Did Escher feel that he had more in common with mathemeticians or with
f) Name one mathematician who collaborated with Escher.
- Go back up and click "Escher" on the menu bar again. You should
end up on the same Introduction page as in # 1. Now click on "Trends
in Mathematics" from your choices on the right. There are 7 different
a) Look at one trend and write a brief summary (3 sentences)
about what you learned. Does this area of mathematics relate to Geometry?
- Go back up and click "Escher" on the menu bar one last time. Now
click on the third section, "Escher Tessellations." There are 12
pages of examples to browse through. Each one shows an Escher tessellation
and highlights the starting polygon. Look at two of the twelve examples.
a) Give a description of each tessellation.
b) Identify the starting polygon and what kind of transformation(s) tessellated
Part 4 - Research of Your Choice
- This site is so large that I can't expect you to look at everything. Take
about 10 minutes to browse through the other main topics ("History,"
"Mosaics/Tiling," and "Beyond"). Find 2 interesting pages.
- When you find a page that interests you, stay on this page and email it
a) Go up to the "Mail" icon on your internet program
b) Hold down "Mail" with one click and a dialogue box will appear
with three choices.
c) Choose to "Send Link" by highlighting it and then unclicking
your mouse. You should be taken to a new email message page.
d) Enter my email address: email@example.com
e) The exact web page directions will be in the body of the email. Write two
sentences to me about what you liked about this page. Then send it!
e) Email the second interesting page to a friend in the class. Follow the
same steps as above.