The 5th graders at Fieldston Lower School spend the year studying Medieval cultures. Prevalent in the art and architecture of these cultures is the use of repeat tessellation patterns. From Zelij tile work in Moorish architecture, to the intricate patterns found in the vaulted ceilings of French cathedrals, geometric polygons are repeated in a variety of patterns.

A tessellation is a repeated polygon and/or combinations of polygons on a two dimensional plane. Each tessellated tile fits perfectly next to its adjacent twin. A true tessellation could repeat infinitely in all directions.The word is derived from the Latin word tessella. A tessella is the individual stone in Roman mosaic.

Working in their classrooms, the 5th graders designed repeat tessellations using pattern blocks. The students traced their patterns on to paper and brought them to the computer lab.

Using the Microworlds program, the students programmed in the six pattern block shapes. These shapes were a square, a triangle, a hexagon, a trapezoid, and two rhombuses. The 5th graders made sure the sides of each polygon were equivalent.

The following is the procedure to create the hexagon:

to hex

pd

repeat 6 [fd 50 rt 60]

end

The next step was to write a procedure or program that joins the various polygons together. The challenge is to place the turtle on the desired corner and at the desired angle to line up the next polygon. Fortunately all the polygon sides are the same distance (with the exception of one side of the the trapezoid which is double the other sides). Also helpful is that all the angles of the polygons are multiples of 30 degrees.

Once the Tessellated pattern is complete, the 5th graders ran the program on a blank page. Using the painting tool, the students copied the image and pasted it on to the page making sure to line it up with the other tile. This is repeated until the page is full. The paint bucket is used to fill in the polygons to create a repeat pattern.

When the students finished their tessellation, many created a second tessellation using additional polygons based upon Islamic tile work from the middle ages. The computer teacher printed all the tesselations on rice paper, mounted them in black frames and placed them in the computer lab windows to create a room of stained glass.

The following is a sample program by a student:

TO TESS

CG PD

HEX LT 60 TRI REPEAT 5 [RT 60 FD 30 TRI]

LT 120 FD 30 LT 120 RHOM2

REPEAT 5 [RT 60 FD 30 RT 60 FD 30 LT 120 RHOM2]

LT 60 FD 30 TRAP

REPEAT 5 [RT 180 FD 60 TRAP]

END