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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 l.jpg

Tessellations and Art

Student Support Services


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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!


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