The Geometer's Sketchpad and Tessellations
Cathi Sanders
Punahou School, Honolulu, Hawaii
Tessellation Tutorials 
Student
Sketchpad Tessellations 
Suzanne's Math
Lessons
Construct a parallelogram, using Parallel Line in the Construct menu. 

Construct a random shape on the left side of the parallelogram. 

Select D and then C, and Mark Vector "D>C" in the Transform menu. Then
select all of the random shape and Translate it By Marked Vector using the Transform
menu. (Vector is the name for a segment with a given length and a given direction.) 

Construct a 2nd random shape on the top of the parallelogram. 

Mark D to A as a vector, and translate the 2nd random shape. 

Select the vertices of your polygon in consecutive order and Construct Polygon Interior 

Translate the whole polygon (vertices, sides and interior) by a vector DC and then
by a vector DA to create a tessellation. Use different colors for adjacent polygons.
Drag any point to change your tessellation. 
You may download and experiment with the sketch, or try a JavaSketchpad version.
[Download ToTessellate.gsp]
