"Understanding symmetry is essential to the understanding of Escher art
and understanding symmetry involves a familiarity with the movements that
mathematicians call transformations." (Jill and Walter Britton)
Click to view the "Step by
Step Tessellations" for a detailed explanation on tessellations.
Click to print the "Step by
Step Tessellations" for a detailed explanation on tessellations.
Vocabulary:
- Tessellation - A tessellation is a pattern of one or more shapes,
completely covering a two-dimensional plane. Picture a puzzle with
pieces that have the same shape and size that fit together perfectly as in
a square. (A circle would not be a shape for a tessellation because
circles cannot fit together in a puzzle.) A tessellation is a pattern
that is repeated. If we take squares and layer them on the floor, we
can cover the entire floor with them, without any space leftover.
- Plane - Imagine a plane to be a tabletop with no thickness that
continues infinitely in all directions.
- Translation - If we move a figure to a new location by sliding it a
fixed distance in a fixed direction, the motion is called a translation.
- Rotation - If we move a figure to a new location by turning it about
a fixed axis, the motion is referred to as a rotation or a turn. Center of
Rotation - The point or axis about which a figure is rotated is called the
center of rotation. The angle through which the figure turns is called
the angle of rotation.
- Reflection - If we move a figure to a new location by flipping it
about a fixed line the motion is called a reflection or flip. The
fixed line about which the figure is flipped is called the line of
reflection. (It is called a reflection
because if a mirror were placed along a line the transformed figure would
coincide with the mirror image of the figure in its original location.)
- Glide Reflection - This final transformation combines the motions of
reflection and
translation to move a figure to its new location.
- By flipping it about a fixed line.
- By sliding it at a fixed distance in a direction parallel to that line.
- The motion is called a glide reflection.
Click on the following for a detailed explanation on:
Student Exercises
- Modify the paint function to create a tessellation of
triangles.
- Modify the paint function to create a tessellation of
hexagons.
- Modify the paint function to create a tessellation of
octagons and squares.
Links about tessellations:
World of Escher
Han's Computer
Art
Swarthmore Tessellation Tutorials
Glide Reflections Tutorial
Movies on
Tessellations
Swarthmore Discussions Thread
Student Work
with Tesselmania
Student Work
with Paint Programs
Lesson Plan
You can contact me at :
roseann@krane.net
Web site
