By Roseann Krane, Monte Vista HS, Danville, CA, and

students: Jefferson Ng, Mike Carns, and Amber Bullington, and

Sherida Hare, Bellport HS, Brookhaven, NY, editor

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:

- Step by Step Tessellations.
- How to use Java to create Tessellations
- Seeing the Tessellation Example of diamonds done with Java
- Seeing the Java Tessellation source code.

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.

Lesson Plan

You can contact me at : roseann@krane.net

Web site