


 The
Topic:
 Tessellations

 Easier  A
tessellation is created when a shape is repeated
over and over again. All the figures fit onto a
flat surface exactly together without any gaps or
overlaps.

 Harder  A
tessellation is a repeating pattern composed of
interlocking shapes (usually polygons) that can be
extended infinitely. The tiling for a regular (or
periodic) tessellation is done with one repeated
congruent regular polygon covering a plane in a
repeating pattern without any openings or overlaps.
Remember 'regular' means the sides of the polygon are
all the same length, and 'congruent' means that the
polygons fitted together are all the same size and
shape. A semiregular (or nonperiodic) tessellation
is formed by a regular arrangement of polygons,
identically arranged at every vertex point.


 Totally
Tessellated (A ThinkQuest Project)
 http://library.advanced.org/16661/index2.html
 Website gives a comprehensive introduction to
tessellations, explaining the basic mathematics
underlying tessellations, as well as allowing you
to browse through many examples of tessellations in
real life. Note: The gallery section contains an
unmoderated student forum.

 Tessellation
Tutorials (A Math Forum Web Unit by Suzanne
Alejandre)
 http://mathforum.org/sum95/suzanne/tess.intro.html
 This site explains what they are, the math
concepts involved, the historical and religious
connection, and provides tutorials and templates
for making your own tessellations. Also provides
numerous links to related resources.

 Tessellation
 http://www.hbschool.com/glossary/math/definitions/tessellation7.html
 Contains an brief, clear and concise
introductory definition along with an animated
graphic.

 Karen's
Tessellation Page
 http://www.coolmath.com/tesspag1.htm
 What are tessellations?


 Find Tessellations in the
World. After exploring the Tessellation
Tutorial and Tessellation
sites, find tessellated shapes in everyday
life. You might start by looking for
patterns in manmade materials, artwork,
architecture, and the like. What about
neartessallations, designs and patterns
that do not perfectly match the
definitions? Take photographs of your
findings and put together a display of the
results. Can you identify the time period
in which they were created? Did you find
some tessellations in nature? There are
some (honeycomb). For some examples of
manmade tessellations, look in the
gallary section at Totally
Tessellated.

 Construct Your Own
Tesselations. Make your own
tessellations. You can follow instructions
found at Tessellation
Tutorials and Creat
Tesselations using ClarisWorks.
Decorate your creations by adding
attractive colors and design shapes. Show
your completed tessellations.

 Compare and Judge
Tessellations. Find and look at many
tessellations. You can find lots of
examples at the websites below. Remember
to check some of the linked sites also.
Pick and choose the best or your favorite
design. Print out and display your
choice(s). Explain why you like and chose
the tessellation as being best.

 Make a Tessellation Quilt
Block. Design and construct a quilt
block that uses a tessellated pattern.
Display the finished work.


 Create
Tesselations Using ClarisWorks
 http://mathforum.org/sum95/suzanne/cwtess.html
 Create computergenerated tesselations using
ClarisWorks

 Tessellations
Step by Step
 http://www.wsd1.org/lgc98/teach/Paint/makefish.htm
 Contains instructions for creating tessellating
art using Paintbrush or Paint software on
Windows

 Tessellate
 http://www.shodor.org/interactivate/activities/tessellate/index.html
 Allows you to generate a new tessellating shape
starting from a rectangle, triangle or
sexagon.

 How
to Create a Tessellation
 http://arttech.about.com/c/ht/00/07/How_Create_Tessellation0962934009.htm?am=dpile&terms=Weaving+Tessellations
 A simple how to on creating tessellations.

 World
of Escher
 http://www.WorldOfEscher.com/
 Learn more about the life and work of M.C.
Escher, a Dutch graphic artist, recognized for
spatial illusions, impossible buildings, repeating
geometric patterns (tessellations), and his
incredible techniques in woodcutting and
lithography.
 Another Escher site:
 http://www.mathacademy.com/pr/minitext/escher

 Tessellations
 http://www.tessellations.com/
 Explore the world of tessellations.

 Student
Tessalations
 http://mathforum.org/alejandre/students.tess.html
 Samples of student work.

 Examples
of Tessellations
 http://www.iusb.edu/~abrown/tessellations.html

 Tantalizing
Tessellations Grade 5
 http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html
 Mainly for teachers; a series of lesson plans
involving tessellations

 Investigations
of Tessellations
 http://mathforum.org/sum95/suzanne/active.html
 Investigating tessellations using pattern
blocks links to activities using pattern blocks in
colour.


'tiling'

dissection

vertex

shape

congruent

quilt

pattern

border

geometry

M.C. Escher

reflection

direction

graphic

embellishment

plane

polygon

translation

rotation

color

irregular

design

interlocking

intersection

computergenerated

angle

mosaic

infinite

edge

periodic

symmetry


 Created by
Annette
Lamb and
Larry
Johnson,
1/99. Updated by
Nancy
Smith
3/02
