M. C. Escher
1898 - 1972
Born in the Netherlands
Escher was a Dutch graphic artist
Today a graphic artist is also known as a
GRAPHIC DESIGNER.
A Graphic Artist
creates the graphics for…
Published materials
A Graphic Artist
creates the graphics for…
Published materials
Printed Materials
Electronic Media - Internet
Movies
Brochures
Advertising
Escher’s Works
• WOODCUTS
– Illustrations produced when the original
printing plate was engraved on a block of
wood.
– This was one of the oldest methods of
printing, dating back to the 8th century China.
“Relativity”
Ants Mobius Strip
A Woodcut Self Portrait
Escher’s Works
• Woodcuts
• LITHOGRAPHS
– A method for printing on a smooth surface.
– It can be used to print text or artwork onto
paper or another suitable material.
“Drawing Hands”
“Waterfall”
Escher’s Works
• Woodcuts
• Lithographs
• IMPOSSIBLE CONSTRUCTIONS
Tribar
Another Tribar
Tessellation
A tessellation is a
collection of polygons
that fit together to cover
a flat surface with no
overlaps and no gaps
Rhombus, Triangle, Trapezoid
creating a TESSELLATION
Squares making a TESSELLATION
Hexagons or Rhombus? They
create a TESSELLATION
We Can
Make a
Tessellation
We will
need….
A Polygonal Shape
Pencil
Paper
Scissors
Tape
Imagination
TESSELLATIONS
Using Pattern Blocks
Take some Squares
Put them together so they touch
side to side
A Tessellation made
of Squares
Take some Triangles
Put them together so they touch
side to side
A Tessellation made of
Triangles
A Tessellation made of
Hexagons
A Tessellation made
with Two Types
Two Different Pattern Blocks
Two More Pattern Blocks
A Tessellation made of
Several Types
Examples of
Escher Tessellations
Another TESSELLATION
How to Create
an Escher
Tessellation
Tessellation Using a
Slide on a Square
Start with a Square
Cut out a Nibble Piece from
one corner to the other
Slide the Nibble Piece to the
opposite side and tape it on
Let’s Add More to Our Piece
Cut out a nibble piece on the uncut
side, slide it to the opposite side,
and tape it on
Another Example of a Slide
This time cut from the corner of the
square to the center, slide and tape
it to the uncut side
Review
The Finished Piece
Add a Bit of Color!!
We could use other polygons
besides Squares.
A Slide on a Rectangle
A Slide on a Hexagon
One Simple Slide
Do You See the Slides?
Do You See the Slides?
You Could Do This One!!
Tessellations using a Turn
(also known as a Rotation)
Start with a Square
Cut a nibble piece out
of one side of your
square
Now TURN (or rotate)
this piece around the
corner, so straight
edges touch
Rotate Around This Point
We Can Even Do Another Turn
Turning Around the Midpoint
• Cut from a corner of the square to the
MIDPOINT of the side
• Turn the piece around the midpoint, tape
Another Example of a Turn
• Cut from a side to the midpoint of the side
• Turn the piece around the midpoint, tape
The Final Piece
Review
The Finished Project
Rotation around Midpoint of the
Sides of Equilateral Triangle
Another Rotation around Midpoint
Rotation around Vertex of Hexagon
Elephant-Seal Tessellation with a
TURN
Moo!!
Lizard, Fish, Bat (by Escher)
Butterflies (by Escher)
STRETCH YOUR
IMAGINATION
Birds or Fish???
Meow
Sky and Water (by Escher)
ESCHER CONTEST
Chicken in A Suit (13 year old)
Tiger (8 year old)
Happy Frogs (13 year old)
Autumn Leaves (12 year old)
Fish (10 year old)
Dogs (10 year old)
Frog Mania (10 year old)
Not Fussy Kitty (9 year old)
High Flying Kite (7 year old)
Rainbow Fish (11 year old)
Angels (11 year old)
Transformational Geometry
•
•
•
•
Reflection – Flip
Translation – Slide
Rotation – Turn
Glide Reflection
REFLECTION (FLIP)
• A reflection transforms an object into its
mirror image
Reflection - Flip
• http://www.misterteacher.com/abc.html
TRANSLATION (SLIDE)
• A translation moves every point by a
fixed distance in the same direction.
Translation – Slide
• http://www.misterteacher.com/abc.html
ROTATION (TURN)
• A rotation moves an object around a
given fixed point.
Rotation - Turn
• http://www.misterteacher.com/abc.html
GLIDE REFLECTION
• A glide reflection is the combination of a
reflection in a line and a translation along
that line.
Glide Reflection
End
Translation
Start
Reflection
Your possibilities of
creating tessellations
are endless.
Have fun with your
creations!!!