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Tessellations and Art . Student Support Services. 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. Types of Tessellations. Regular Tessellations Semi-regular Tessellations. Regular Tessellations.

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tessellations and art

Tessellations and Art

Student Support Services

what is a tessellation
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
types of tessellations
Types of Tessellations
  • Regular Tessellations
  • Semi-regular Tessellations
regular tessellations
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.

semi regular tessellation
Semi-regular Tessellation
  • They are made using two or more different regular polygons.
tessellations and math
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.
types of symmetry in math
Types of symmetry in Math
  • Rotations
  • Translations
  • Reflections
  • Glide reflections
rotation
Rotation
  • To rotate an object means to turn it around a point at a certain angle. This point is called the center of rotation.
translation
Translation
  • To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance.
reflection
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".
glide reflection
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.
a few uses of symmetry
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
how is tessellations used in art
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!

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