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# Tessellations and Art - PowerPoint PPT Presentation

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

Student Support Services

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

• Regular Tessellations

• Semi-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.

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

• Tessellations use symmetry in Math.

• Symmetry means that at least one pattern is unchanged.

• There are four types of Symmetry in the plane.

• Rotations

• Translations

• Reflections

• Glide reflections

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

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

• 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".

• 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.

• Patterns for shoe bottoms.

• Parking lot design.

• Design color pattern for neckties and t-shirts.

• Design wallpaper for interior decoration

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?

Then the artist tessellated it.

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

Here is another example. What does this look like?

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

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

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