Tessellations Project Final
Tessellations Project Final
Tessellations Project Final
Intro to Geometry
Maurits Cornelis Escher, born in Leeuwarden, Holland in 1898, created unique and fascinating works
of art that explore and exhibit an array of mathematical ideas. Among his greatest admirers were
mathematicians, who recognized in Eschers work an extraordinary visualization of mathematical
principles. This was quite remarkable as Escher had no formal mathematics training beyond
secondary school.
Tessellations, or regular divisions of the plane, are arrangements of closed shapes that completely
cover the plane without overlapping and without leaving gaps. For shapes to fill the plane without
overlaps or gaps, their angles, when arranged around a point, must have measures that add up to
exactly 360. Typically, the shapes making up a tessellation are polygons or similar regular shapes
(like square tiles used on floors). Escher exploited these basic patterns in his tessellations, applying
reflections, translations, and rotations to obtain a greater variety of patterns. He also distorted
these shapes to form animals, birds, and other figures.
Project Objective: Students will create a tessellation that demonstrates their knowledge of the
properties of geometric transformations, such as translations, rotations, and
reflections.
Procedure:
Tessellation
Use one or more transformations to create a Tessellation on 8.5" x 11" paper (standard
computer paper).
You will need to make a template to trace. There are complexity points for your tessellation. You
get more points for attempting a more difficult tessellation. You may not simply take a polygon and
slide, rotate, or reflect it over and over again to create your tessellation. You must create a
template based on one of the methods in this packet.
**You can use the computer to create your template, but the tessellation must be drawn by hand.
Written Response
Type a 1-page response that specifically answers each of the questions below:
1. What is the idea/theme behind your tessellation?
2. What polygon(s) did you start with and how did you alter it?
3. What transformations did you use?
4. In your opinion, are tessellations math or pieces of art? Justify your answer.
5. Provide some examples of where tessellations are found in the world around us. For example, look
for examples in nature, art, architecture, business, or advertising. Include two photos or a printout
of two pictures to support your claim.
Your response needs to be typed and in complete sentences!
**You may work in pairs or individually for this project. For those students working in pairs, both
students will receive the same grade. So, choose your partners carefully!
**Use the Project Planning Worksheet to generate ideas and help focus your project on a specific
theme. Remember, you are creating an original piece of work.
Assessment:
Tessellation
y Polygon(s) and transformations used
y Complexity and creativity
y Visual appeal (neatness and color)
y Follows directions (meets project requirements)
Written Response
20 pts.
20 pts.
TESSELLATION RUBRIC
4
Organization
Tessellations are
presented in an
organized manner.
Their construction is
complete and
accurate.
Tessellations are
Tessellations are
presented in a
organized, but not
somewhat organized well constructed.
manner. Their
construction is fairly
complete.
There is no
organization to the
tessellation.
Complexity
of Design
Tessellation was
created with nonpolygon shapes that
connect to create an
intricate and
complex pattern.
Tessellation was
created with complex
polygon shapes that
connect to create an
intricate and
complex pattern.
Tessellation was
created with simple
shapes that connect
to create a pattern
Tessellation is
simple and pattern is
not complex or
interesting.
CATEGORY
covered by the
complex pattern to
completely fit
together.
Creativity
Tessellation uses
unique design and
patterns of unusual
shapes to form a
complex and
interesting design.
Tessellation uses a
mixture of polygons
and interesting
shapes to create a
nice design.
Tessellation uses
There is no creativity
some shapes that fit to the design.
together to form a
simple pattern
Follows
Directions
Tessellation covers
an 8.5"x11" sheet of
paper completely
with interesting
display and
presentation.
Tessellation covers
an 8.5"x11" sheet of
paper and has a
complete
presentation.
Tessellation mostly
covers an 8.5"x11"
sheet of paper and
has no presentation
Tessellation does
not cover the
8.5"x11" paper
completely.
How are you going to use color to alter your tessellation and create more patterns?
What is the idea or theme that you want to express in your piece?
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Translation Tessellation (Easy) Template
For simple translation tessellations, the starting polygon should have opposite sides that are parallel
and congruent. Squares, hexagons, and parallelograms work best here.
Example:
1. Start with a square.
3. Cut the design piece out and translate (slide) it across to the opposite side of the square. Secure it
there with tapebe careful not to overlap the piece or make a gap. It should fit perfectly at the
seam.
Seam >
1. Start with
a square.
2. Draw a
design on
one side of
the square.
1. Start with
a square.
2. Draw a
design on
one side of
the square.
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