Tessellations

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Tessellations

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

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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

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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!

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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

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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.

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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

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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.

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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

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Translation

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

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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.

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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.

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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.

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Famous Tessellations

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

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Another Famous One

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

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• 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.