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.

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.

Student Art Section

Faces of the Lady by Liz Kirk

Dog Pound by Darrin Bruening

R2D2 by Eric Broten

Motorcycle Guy by Kevin Herwig

Dogs by Tim Vandenberg

Birds by Bonnie Bueschel

Fish by Becky Franklin

M.C. Escher Section

Lizards

Fish and Boats

Butterflies

Sun and Moon

Let’s Get Started

Tessellating a parallelogram by translating opposite sides

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

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!

Repeat the process with the other 2 sides

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

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!

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

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

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

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

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

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

Tessellating any quadrilateral by rotation about midpoints

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

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

Repeat the process carefully with the next side...

Repeat the process with the two remaining sides.

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

The End... Or just the beginning!