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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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