INTERNET EXPLORATION - TOTALLY TESSELLATED

Totally Tessellated is an award-winning internet site that has some amazing graphics and instructions about tessellations. It was designed by a group of students. Follow the directions below, and write out your answers on a separate sheet of paper
Have fun!

Take your time. Read each entry and enjoy viewing the different examples and interactive displays.

  1. If you are not already at this location, go to http://library.thinkquest.org/16661/sitemap.html
    Enter the site. There is a clickable site map.
    If you get lost, you can always go to the site map by selecting the site map hypertext link that is available at the top of every page.

    At the bottom of every page, there are three triangle: a left arrow to go backward, an up arrow to go to the next category, and a right arrow to go forward.
    If you can, go forward. If this triangle is not available, go to the next category.

    WRITE ALL OF YOUR ANSWERS ON A SEPARATE SHEET OF PAPER!


  2. Go to the "In Mathematics and Science" location.
    1. How have tessellations been used in mathematics?
    2. How have tessellations been used in science?


  3. Go to "Decorative Uses, Ancient and Modern"
    1. How far back have the use of tessellations been traced?
    2. Which cultures have used tessellations?

  4. Under the Historical Image Gallery, real images of tessellations are pictured and described. Select "Time Periods". Describe one real example of a tessellation from each of the time periods listed below. Include the location, colors, date, and any other pertinent data.

    1. 11th - 14th century
    2. 12th - 13th century
    3. 16th century
    4. 17th - 18th century
    5. 19th - 20th century

  5. Go the the "Cultures" site. Describe one real example from each of five cultures. Use examples you haven't already described.
    1. Culture 1
    2. Culture 2
    3. Culture 3
    4. Culture 4
    5. Culture 5

  6. The Essentials sections is designed as a tutorial to teach all there is to know about constructing tessellations. It will be helpful for you when working on your tessellation project. Work through all of the sections.

    Many of the sections contain animated segments that will help you visualize the concepts. There are also many "hands-on activities" sections. You may print these off and try them as you work along.

  7. Begin by reading about "Polygons and Angles"
  8. Now select "Symmetry and Transformations"
    .
    1. Select "Translations". Use the java applet to try the technique. Describe one real example from this section.
    2. Select "Rotations. Use the java applet to try the technique. Describe one real example from this section.
    3. Select "Reflections". Use the java applet to try the technique. Describe one real example from this section.
    4. Select " Glide Reflections". Use the java applet to try the technique. Describe one real example from this section.
    5. Select "Hands-on-activity". confirm translations symmetry, using this activity.

  9. Go the the section "Regular Polygons" (still under the Background Information)
    1. Describe a real tessellation formed by a regular polygon.
    2. What is the difference between a true tessellation and a repeating pattern that is not a tesselation? Sketch an example of each.

  10. Go the the section "Color Usage"
    1. What are warm colors? What are cool colors?
    2. What is meant by the value of a color?
    3. Give one real example of a coloring technique.
    4. Describe each of the four coloring techniques that are discussed in this section.

  11. Read the sections "Regular Tessellations" and "Semiregular Tessellations" under Simple Tessellations with Regular Polygons.
    1. What is the difference between regular tessellations and semiregular tessellations?
    2. Why is it that among regular polygons, we can only tessellate with triangles, squares, and hexagons?
    3. How do we name tessellations? Sketch an example.
    4. How are semi-regular tessellations different from regular tessellations?
    5. How many different arrangements of polygon tessellations are there?
    6. How many different combinations of polygon tessellations are there?

  12. Go tho the section "Triangles"under the section Simple Tessellations with Non-Regular Polygons.
    1. Explain and sketch the two techniques you can use to guarantee that non-regular triangles will tessellate.

  13. Go to the section "Quadrilaterals".
    1. Give one example from this section.

  14. Go to the section "Mosaics/Tilings, Tilings of Non-Regular Polygons,Pentagons".
    1. Sketch and describe limited technique 1.
    2. Sketch and describe limited technique 2.

  15. Go the Escher section. Begin by readiing his "Biography".
    1. Briefly describe who Escher was, and what people/schools/cultures influenced him.

  16. Read through and view each of the sections under "Trends in Escher's Work". For each section, discuss one print. Give the title, and explain the mathematics you see in it. (Use terminology like reflection, glide reflection, rotation, translation, perspective, etc.)
    1. Polyhedra
    2. Infinity
    3. Knots
    4. Perspective
    5. Mirrors
    6. Impossible Architecture
    7. Tessellations