Kevin Sutton

1
Tessellations
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• By
• Kevin Sutton
• Isadora Rivers

2
Explanation of a Tessellation

• A tessellation is made when a shape is repeated
  covering a plane without any gaps or overlaps.

3
How do We Know That a Shape Tessellates

• We know that a shape will tessellate if it
  tessellates by it self. If the sides dont
  overlap and there are no gaps then the shape can
  tessellate.

4
An explanation of each type of transformation and
how they are used in tessellations

• Rotation
• A rotation is a transformation in which a figure
  turns around a fixed center point. A rotation
  does not change the figure. A quarter turn is a
  rotation of 90. A half turn is a rotation of 180
  .
• Reflection
• A reflection is a transformation in which a
  geometric figure is reflected across a line,
  creating a mirror image. A reflection changes the
  order of points as one goes around the figure.

5
An explanation of each type of transformation and
how they are used in tessellations

• Translation
• Without any change in size or orientation, a
  translation is the transformation in which a
  geometric figure is moved to another location.
• Tessellation
• Without overlapping or leaving blank spaces, a
  tessellation is to cover a plane with identically
  shaped pieces.

6
An explanation of each type of transformation and
how they are used in tessellations

• Dilation
• A dilation is the transformation in which a
  geometric figure either enlarges or becomes
  smaller. This has to do with the center of
  dilation and a scale factor.

7
A slide show of art work from Escher that clearly
illustrates each transformation

• This Tessellation clearly uses the
  transformations of reflection, and translation.

8
A slide show of art work from Escher that clearly
illustrates each transformation

• This tessellation clearly uses the transformation
  of rotation and translation.

9
A slide show of art work from Escher that clearly
illustrates each transformation

• In this tessellation the transformation used is
  clearly the one of translation.

10
A slide show of art work from Escher that clearly
illustrates each transformation

• This Tessellate clearly uses the transformations
  of rotation and translation.

11
A slide show of art work from Escher that clearly
illustrates each transformation

• One transformation this tessellation clearly uses
  is the one of dilation.

12
A slide show of art work from Escher that clearly
illustrates each transformation

• This tessellation clearly uses the
  transformations of dilation, reflection,
  rotation, and translation.

13
A slide show of art work from Escher that clearly
illustrates each transformation

• This tessellation clearly uses the
  transformations of rotation and translation.

14
A construction of each type of transformation

• Rotation
• This is a rotation of 120

• Reflection

15
A construction of each type of transformation

• Tessellation This is a tessellation of
  triangles.

• Dilation This is a dilation by 0.5.

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A construction of each type of transformation

• Translation This shape is translated by 5 cm.