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Tessellations

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Title: Tessellations


1
Tessellations
  • A guide for 4th 5th graders
  • By Sarah Gottschalk

2
Who created tessellations?
  • The man who first drew and developed
    tessellations was a man named Maurits Cornelis
    Escher, from Leeuwarden, Netherlands. The
    picture on above is his self portrait.
  • More history on Escher can be found by going to
    this site Tessellations - M.C. Escher 1

3
What is a Tessellation?
  • A tessellation is a figure or combination of
    figures in a plane of regular repetition of the
    figure or figures that covers the plane so that
    there are no gaps and no overlapping of figures.
  • There are several kinds of tessellations,
    including regular and semi-regular
  • Coolmath.com - Karen's Tessellation Page!

4
Regular Tessellations
  • These kinds of tessellations are created using
    regular polygons.
  • The only three regular polygons that can
    tessellate are
  • Equilateral triangles
  • Squares
  • Regular hexagons

5
Semi-regular Tessellations
  • These are tessellations that have two or more
    regular polygons that are arranged so that the
    same polygons appear in the same order around
    each vertex point.

6
Tessellation Rules
  • The tessellation must be able to tile a floor,
    with no overlapping or gaps.
  • All tiles must be the same.
  • Each vertex must look the same

7
Why do we need to learn about tessellations?
  • Tessellations are helpful when you are learning
    geometry, because it helps you learn about
    symmetry.
  • Its fun!
  • It combines math with art, which is important to
    learn how things are interconnected.
  • So you can spot tessellations in the real world
    and know how to identify them.

8
The 4 symmetries in tessellations
  • In all tessellations, there are 4 basic patterns
    of symmetry that are used.
  • The symmetries are movement, without distortion
    of the size or shape of the original shape.
  • The kinds of symmetries are translations (or
    slides), reflections, glide reflections, and
    rotations

9
Translation
  • The figure at the right is an example of a
    translation.
  • This is also known as a slide

10
Reflection
  • This is an example of a reflection.
  • A good way to remember this is to think of it as
    a reflection in a mirror.

11
Glide Reflection
  • In this symmetry, the shape is just flipped
    upside-down.
  • This one is probably the hardest to remember
    because the name doesnt give it away like the
    others do.

12
Rotation
  • The shape here is not only flipped upside-down,
    but also it is reflected, like you are looking at
    it upside down in a mirror.

13
Famous Tessellations
  • This is one of Eschers most famous
    tessellations. It is simply called Reptiles

14
Another Famous One
  • Another one of Eschers famous tessellations is
    this one, called Elephants
  • To find more go to Hop's Escher Tessellation
    Tiles

15
  • So, as you can see, tessellations are fun to
    learn about and easier to replicate than perhaps,
    you originally thought, so now its you turn to
    create your own.
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