1. Tessellation Project Created by Jim Geisthardt
Graphic images created with The Geometer’s Sketchpad
Student images produced by hand.
All M. C. Escher works (C) Cordon Art, Baarn, the Netherlands. All rights reserved. Used by permission.

2. Before the lesson begins, we’ll take a look at some student work that was created using these techniques and some works by the artist
M.C. Escher.

3. Student Art Section

4. Faces of the Lady by Liz Kirk

5. Dog Pound by
Darrin Bruening

6. R2D2 by Eric Broten

7. Motorcycle Guy by Kevin Herwig

8. Dogs by Tim Vandenberg

9. Birds by Bonnie Bueschel

10. Fish by Becky Franklin

11. M.C. Escher Section

15. Lizards

16. Fish and Boats

17. Butterflies

18. Sun and Moon

19. Let’s Get Started

20. Tessellating a parallelogram by translating opposite sides

21. Start with any kind of parallelogram, here I used a rectangle
Carefully line up points on a pair of opposite sides

22. Cut out sections from side 1, tape to side 2
Make sure that you line up the locations exactly or the shape you make will not tile!

23. Repeat the process with the other 2 sides

24. Try to imagine what your figure looks like!
Give it some color and Be Creative!

25. To tile your shape, start near the center of the paper and trace your shape.
Slide your shape so the edges match and trace again.
Fill the page, draw in your details, and color!

27. Tessellating a parallelogram by rotation about midpoints and translation of opposite sides

28. Start with any size parallelogram.
Locate the midpoints of one pair of opposite sides.

29. Cut out a section from one side of the midpoint.
Rotate the shape 180° about the midpoint and tape it in place.

30. Repeat the process on the opposite side.
Cut out a section, rotate 180° about midpoint and tape in place.

31. As in the previous example, locate matching points on the 2 unchanged sides,
Cut out shapes,
And tape in place on the opposite side.

32. Try to decide what it is that you’ve created.
Add some details
and get ready to tessellate.
Rotate the shape 180° about point K and also about point I.
Translate the shape by sliding along the vector AB

34. Tessellating any quadrilateral by rotation about midpoints

35. Start with any shape quadrilateral
Locate the midpoint of all four sides

36. Cut out a section from either side of the midpoint.
Rotate the section 180° about the midpoint,
And tape into place.

37. Repeat the process carefully with the next side...

38. Repeat the process with the two remaining sides.

39. To make the shape tessellate…
Rotate each side about its midpoint.
Start in the center of the page and
ROTATE!

45. The End...
Or just the beginning!