6A Symmetry

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6A Symmetry
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Line Symmetry

• Shape has line symmetry when one halfof it is
  the mirror image of the other half.
• Symmetry exists all around us and many people see
  it as being a thing of beauty.

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Is a butterfly symmetrical?
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Line Symmetry exists in nature but you may not
have noticed.
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At the  beach there are a variety of shells with
line symmetry.
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Under the sea there are also many symmetrical
objects such as these crabs and this
starfish.
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Animals that have Line Symmetry

• Here are a few more great examples of mirror
  image in the animal kingdom.

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THESE MASKS HAVE SYMMETRY

• These masks have a line of symmetry from the
  forehead to the chin.  
• The human face also has a line of symmetry in the
  same place.

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The Taj Mahal

• Symmetry exists in architecture all around the
  world.  The best known example of this is the Taj
  Mahal.

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TransmoGrapher
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See It 
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Transformations
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kali
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Symmetry and Pattern - Oriental
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Symmetry from Australia
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Kaleidoscope 
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ElabTransformations
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What are tessellations? Basically, a tessellation
is a way to tile a floor (that goes on forever)
with shapes so that there is no overlapping and
no gaps. Remember the last puzzle you put
together? Well, that was a tessellation! The
shapes were just really weird.
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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.
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Construct a parallelogram.
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Construct a random shape on the left side of the
parallelogram
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Select D and then C, and Mark Vector "D-gtC" in
the Transform menu. Then select all of the random
shape and Translate it By Marked Vector using the
Transform menu.
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Construct a 2nd random shape on the top of the
parallelogram.
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Mark D to A as a vector, and translate the 2nd
random shape.
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Select the vertices of your polygon in
consecutive order and Construct Polygon Interior
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Translate the whole polygon (vertices, sides and
interior) by a vector DC and then by a vector DA
to create a tessellation. Use different colors
for adjacent polygons. Drag any point to change
your tessellation.
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JavaSketchpad Tessellations
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ROTATION is another technique. It is shown here
using an equilateral triangle.
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Tesselations
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Rotational Tessellation
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Translational Tessellation
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Contest
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