Tessellations
Art and Math…
How are they related?
Art and Math…
How are they related?
One way art and math are related is through
the manipulation of shapes.
• In math, this is called Transformation. The term
refers to four specific ways to manipulate shapes.
• In art, we use Transformation techniques to
create compositions called Tessellations.
What’s a tessellation?
A tessellation uses congruent figures to cover a plane in a symmetrical way
without overlapping or leaving gaps.
Designs featuring animals, birds, etc. which can fill a page without overlapping
to form a pattern (or mosaic).
origami
honeycomb
concrete patio tiles
Uses for tessellations…
Talk with your “elbow partner” and identify some uses for
tessellations.
Be ready to tell me what your partner said.
Tessellations have been seen throughout art
history, from ancient architecture to modern art.
artist M.C. Escher
dutch 1898-1972
M.C.Escher said, "Mathematicians
go to the garden gate but they
never venture through to appreciate
the delights within."
1958 Circle
Limit III
Sky & Water, woodcut
Early work of M.C.
Escher
1936 Strong Men
1938 Fish
1938 Dogs
1937 Lions
artist Robert Fathauer
american, born 1960In 1993, he founded a business, Tessellations, to produce
puzzles based on his designs. Over time, Tessellations'
product line has grown to include mathematics
manipulatives, classroom posters, and books as well.
Three Fishes, 1994
Marathon, 2004, commissioned for the Chicago marathon
Types of Tessellations
1- Translation- moving every point of the
figure the same distance in the same
direction
2- Rotation- rotating the figure from a single
point
3- Reflection- reflecting every point of the
figure over an axis, as if looking in a mirror
Let’s practice…
TRANSLATION
1- Draw a line from the TOP RIGHT corner to the TOP LEFT corner.
2- Draw a line from the TOP LEFT corner to the BOTTOM LEFT corner.
3- Cut out – now you will have 3 pieces.
4- Slide the TOP piece to the bottom and tape down.
5- Slide the LEFT piece to the right and tape down.
6- Align the original corners of the new ‘transformed’ shape with the grid corners in the upper left
box of the grid paper.
7- Trace once.
8- Slide shape to the right; trace.
9- Slide shape to the bottom; trace.
ROTATION
1- Draw a line from the TOP RIGHT corner to the TOP LEFT corner.
2- Draw a line from the TOP LEFT corner to the BOTTOM LEFT corner.
3- Cut out – now you will have 3 pieces.
4- Rotate the TOP piece counter-clockwise holding down the TOP RIGHT corner; ending up on
the right side. Tape down.
5- Rotate the LEFT piece clockwise holding down the BOTTOM LEFT corner; ending up at the
bottom. Tape down.
6- Align the original corners of the new ‘transformed’ shape with the grid corners in the upper left
box of the grid paper.
7- Trace once.
8- Hold down the TOP RIGHT corner and rotate counter-clockwise. Realign corners; trace.
9- Hold down the LOWER RIGHT corner and rotate counter-clockwise. Realign corners; trace.
10- Hold down the BOTTOM LEFT corner and rotate counter-clockwise. Realign corners; trace.
Let’s practice…
REFLECTION
1- Draw a line from the BOTTOM RIGHT corner to the BOTTOM LEFT corner.
2- Draw a line from the BOTTOM RIGHT corner to the TOP RIGHT corner.
3- Cut out – now you will have 3 pieces.
4- FLIP over the RIGHT PIECE (from top to bottom), then slide to the left side. Tape down.
5- FLIP over the BOTTOM PIECE (from right to left), then slid to the top. Tape down.
6- Align the original corners of the new ‘transformed’ shape with the grid corners in the upper left
box of the grid paper.
7- Trace once.
8- FLIP over the shape (from top to bottom), then slide to the RIGHT. Trace.
9- FLIP over the shape (from top to bottom), then slide to the RIGHT. Trace.
10- FLIP over the shape (from right to left), then slide DOWN. Trace.
11- FLIP over the shape (from top to bottom), then slide to the LEFT. Trace.
Which type of
tessellation is this
artwork?
M.C. Escher
Which type of
tessellation is this
artwork?
Robert Fathaurer
Your turn…
1- Choose one of the 3 types of Tessellations
to practice on your own.
2- Flip your grid paper over and trace the grid.
(if you choose Reflection, trace the 6 box
grid).
3- Trace once in the upper left box.
4- Move the shape around the page according
to the Tessellation method you chose.
Project: Tessellation
Create a unique artwork using one of the 3
tessellation methods learned.
1- Completely cover a 12” x 18” page.
2- Use 2 or more colors.
3- Add hand-drawn details to create a
recognizable figure.
Assessment Rubric
Assignment: Tessellation
•
Criteria 1 –Technique- 20 points - Did student successfully tessellate a
plane using on of the 3 methods of translation, rotation, or reflection?
•
Technique – Placement - 20 points - Did student correctly line-up shapes
to eliminate overlapping and gaps?
•
Criteria 2 – Design- 20 points -- Did student effectively use color and
repetition to create a strong design? Did student create a recognizable
object by drawing details?
•
Criteria 3 – Effort- 20 points – Did student use time wisely and try their
best. Did they developed their ideas fully, and also finish their project (didn’t
rush)?
•
Criteria 4 – Craftsmanship- 20 points – Did the student skillfully use art
tools & materials, pay attention to details, and present a neat artwork?
How To Create Your Tessellation
Supplies:
3” x 3” card (for tessellation template)
Pencil
Scissors
Tape
Ruler
Black Felt-tip Pen
12” x 18” white paper
Construction paper of various colors
1- Choose which tessellation method you will use (Translation, Rotation, or
Reflection).
2- PRACTICE making your tessellation template on scratch paper in a 3” x 3” box.
3- Create your tessellation template on the 3” x 3” card, following the directions on
the “Let’s Practice” sheets.
4- Lightly draw 3” x 3” grid on your 12” x 18” white paper.
5- Trace your template once onto your white grid paper.
6- Move your template around the page following the directions on the “Let’s
Practice sheet. Trace each placement. Fill the entire 12” x 18” page.
7- Trace your template onto construction paper and cut out shapes.
8- Glue construction paper shapes onto white grid paper in checkerboard pattern.
9- Erase grid lines from white grid paper.
10- Add detail lines with black felt tip pens (check out from Mrs. Smether’s).