M.C. Escher Tessellations

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. I learned the hard way how easily triangles can get flopped and rotated, so I came up with a numbering process that eliminated that problem.

1. Give each student a 3" (or larger) square of heavy card stock paper, scissors, tape, and drawing paper.
2. Make a diagram on a board that follows the steps illustrated to the right.
a. Number the corners as shown.
b. Cut the bottom two corners off and move up to the top. With edges "kissing" and not overlapping, tape in place. The numbers should stay right reading.
c. The students are to draw a triangle on the back side, label "H" for head, and move to the right top and tape in place to make a bird shape.
3. Using the bird as a tracing template, they are to align it with the side of a drawing paper, and trace one stacking column. Then, if they move the bird to the right and interlock the head shapes, they can make another column that interlocks with the first. Continue tracing columns until the paper is filled.
4. Lastly, pencil lines are traced with a marker and the shapes are colored in. This artwork uses crayon, but painting would look very nice too.

Fish Tessellation

A tessellation is a collection of shapes that fill a paper with no overlaps and no gaps. I like the combination of math and artistic skills they require, and am happy to say that this design is my very own.

1. Start with a card stock square, at least 3" wide. I recommend labeling the four corners as shown in diagram 1. Measure and mark the middle of each side of the square.
2. On the top right corner, draw and cut out a curve, leaving a little flat space that I like to call the “nose”.
3. The top curve piece is flopped and traced to make a symmetrical version below. Cut out the shape.
4. Both curved shapes are aligned and slide to the back of the square as shown. Tape in place. It is VERY important that the numbers read as shown as flopped and rotated shapes will not fit together when complete.
5. Cut one triangle from the bottom of the shape, making it as equilateral as possible. It is slid to the top, aligned with the front of the fish and taped in place.
6. Place your fish on at least a 9" x 12" drawing paper, and trace. It’s best to make one row going across the paper first, and then add rows on top, always interlocking the shapes when tracing. Lastly, trace the lines in black marker and color with crayon. See artwork by M.C. Escher to get inspired for more complex tessellations.