Lesson Plans By Beverly McCarthy & Luis Valderas

Explanation

A simple tessellation is a design created by images placed against each other with no empty spaces in between. The background of this page is a semi regular tessellation . There are regular tessellations and semi regular tessellations.

History

Tessellations have been traced back to ancient cultures and can also be found in the natural world; however, they have had a relatively short history as a topic for serious mathematical and scientific study. One of the first mathematical studies of tessellations was conducted by Johanne Kepler in 1619 who wrote about the regular and semi regular tessellations, which are coverings of a plane with regular polygons.

Near the end of the nineteenth century in 1891, the Russian crystallographer E. S. Fedoro proved that every tiling of the plane is constructed in accordance to one of seventeen different groups of isometries (i.e., methods of repeating tilings over the plane). More recent research has been done using advanced mathematical analyses. Tilings in more than two dimensions and in non-Euclidean geometrical systems have been explored.

M.C.Escher

Maurits Cornelius Escher was born on 17th June, 1898, in Leeuwarden, Netherlands. His father was a civil engineer, and he realized at an early age that his son had a liking for art and drawing. This led him to decide to send Escher to study at the School of Architecture and Decorative Arts in Haarlem. However, Escher gave up architecture in favor of graphic arts at the age of 21. Escher spent a number of years traveling in Europe, while his interest in graphics grew. In 1921 he got married and lived in Rome, Italy. At the time, his works depicted landscapes using impossible perspectives.

In the 1930's, Facism in Italy made life impossible for Escher and his family, so they moved to Switzerland. In 1936, Escher embarked on an important journey to the Alhambra in Granada, Spain. The Moorish tilings he saw there fascinated him, and some time after his visit he read Pólya's 1924 paper on plane symmetry groups. Between 1936 and 1942 Escher produced 43 colored drawings with a wide variety of symmetry types while working on possible periodic tilings. He adopted a highly mathematical approach with a systematic study using a notation which he invented himself.
In 1941, Escher returned to the Netherlands, after spending a while in Belgium. His fame slowly spread, and during the 1950s, articles on his work appeared. His works began to be displayed in science museums rather than art galleries.

Your Assignment

Follow this link to find out your project requirements and criteria.

Directions to make a Tessellation

1. Cut a square out of the tag board. This will be your original object.

2. Select an area of this object and cut it out. DO NOT THROW AWAY THIS PIECE.

3. Tape that section on the other side of the square, at exactly the height you cut it out from. (when cutting from the top or bottom, tape at exactly the same distance in width).

4. Select another section of the square and remove it.

5. Tape it on the other side of the square at exactly the same height you cut it from (when cutting from the top or bottom, tape at exactly the same distance in width).

6. Continue with steps 4 and 5 until you have created an object you would like to use in your final drawing.

7. Place the object on the large sheet of paper and trace it's outline.

8. Place the object next to the outline so that it aligns up perfectly with no empty spaces, and make another outline.

9. Fill up the entire sheet of paper.

10. Now you can color the design and add detail. Consider color schemes to be used on you project.

11. Then you're done.

Examples

iProject Online-Make your own Tessellation

Regular Tessellations

Semi regular Tessellation Examples

Student work

Josh E. Chelsea G. Stephanie V.

Vocabulary Search:

balance                                                                regular polygon
symmetry                                                            hexagon
line                                                                       equilateral triangle
color scheme                                                      square
pattern                                                                  line segment
intersection                                                         point
radial symmetry                                                 area
rotational symmetry                                          measure of angles of regular figures
analogous color scheme                                   complementary colors
monochromatic color scheme                          warm colors
regular tessellation                                            cool colors
semi-regular tessellation
translations

Look it up!!

Resources

Materials Needed:

1. A small amount of heavy duty paper, like tag board.
2. A large sheet of paper where you will put your final design.
3. Tape. Any kind of tape will work - clear cellophane tape works well.
4. A pencil.
5. A pen.
6. Tracing paper (optional).
7. Tempera paint.
8. Paintbrushes (assorted sizes).
9. Permanent black marker.
10. Scissors.

Net Sources

Teacher Page