Tessellations and Art

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Tessellations and Art

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What is a Tessellation?

• It is a tiling of the plane is a collection of
  plane figures that fills the plane with no
  overlaps and no gaps

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Types of Tessellations

• Regular Tessellations
• Semi-regular Tessellations

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Regular Tessellations

• RULE 1   The tessellation must tile a floor
  (that goes on forever) with no overlapping or
  gaps.
• RULE 2  The tiles must be regular polygons -
  and all the same.
• RULE 3   Each vertex must look the same.
• There are only 2 polygons that will work for
  regular Tessellations and those are equilateral
  triangle, hexagon, and a square.

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Semi-regular Tessellation

• They are made using two or more different regular
  polygons.

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Tessellations and Math

• Tessellations use symmetry in Math.
• Symmetry means that at least one pattern is
  unchanged.
• There are four types of Symmetry in the plane.

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Types of symmetry in Math

• Rotations
• Translations
• Reflections
• Glide reflections

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Rotation

• To rotate an object means to turn it around a
  point at a certain angle. This point is called
  the center of rotation.

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Translation

• To translate an object means to move it without
  rotating or reflecting it. Every translation has
  a direction and a distance.

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Reflection

• To reflect an object means to produce its mirror
  image. Every reflection has a mirror line. A
  reflection of an "R" is a backwards "R".

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Glide Reflection

• A glide reflection combines a reflection with a
  translation along the direction of the mirror
  line. Glide reflections are the only type of
  symmetry that involve more than one step.

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A few uses of symmetry

• Patterns for shoe bottoms.
• Parking lot design.
• Design color pattern for neckties and t-shirts.
• Design wallpaper for interior decoration

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How is Tessellations used in Art?

• First, the artist will cut out a shape and then
  will decide what this particular shape looks
  like. For example, what does this look like?

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Tessellations and Art

• Then the artist tessellated it.

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Tessellations and Art

• He thought it looked like a house so he colored
  it in like this

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Tessellations and Art

• Here is another example. What does this look
  like?

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Tessellations and Art

• This is what the artist saw and how he
  tessellated it.

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Tessellations and Art

• You can also take a shape, tessellate it and then
  color it in, like this

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Tessellations and Art

• Now it is your turn! We are going to be doing one
  like the previous one we just saw. Have fun!