Tessellations and Art

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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

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
• 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
• They are made using two or more different regular polygons.
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
• Rotations
• Translations
• Reflections
• Glide reflections
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
• To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance.
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
• 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
• 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?

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?

Tessellations and Art

Then the artist tessellated it.

Tessellations and Art

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

Tessellations and Art

Here is another example. What does this look like?

Tessellations and Art

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

Tessellations and Art

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

Tessellations and Art

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