Difference between revisions of "Reflectional Symmetry"

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[[Category:High School]]
 
[[Category:High School]]
  
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If one side of the image is the mirror image of the other side, then we say the figure has reflectional symmetry. Sometimes we would say that the image has a mirror line. Here we have some images from real life that have such mirror lines. The image on the left is McCarren Park Pool in New York. The red line in the center was added to show you where the mirror line is located. The next image is a piece of a Persian rug. Here again you can see that the left side is an exact mirror image of the right hand side. The bug right next to it also has a vertical mirror line, and the left side is a mirror image of the right side.  The image of the ducks shows that the mirror line can also run in other directions. In the duck picture the mirror line runs from left to right.
  
If points of a figure are equally positioned about a line, then we say the figure has {{define|reflection symmetry}}, or sometimes
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{| Border="1" align="center"
{{define|mirror symmetry}}. The line is called the {{define|reflection line}}, the {{define|mirror line}}, or the {{define|axis of symmetry}}.
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The axis of symmetry separates the figure into two parts, one of which is a mirror image of the other part.
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| [[Image:McCarren-Park-Pool.jpg|250px]] || [[Image:Farsh1.jpg|250px]] || [[Image:Aragaru1.JPG|150px]] || [[Image:Whistling-Duck.jpg|200px]]
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|-
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| McCarren Park Pool || A rug || A Beetle || Ducks
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|}
  
The simplest case of reflection symmetry is known as {{define|bilateral symmetry}}. For example, each of the following figures exhibits bilateral symmetry:
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<br>
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To make the idea of symmetry a bit more precise, we would say that if points of a figure are equally positioned about a line, then the figure has {{define|reflection symmetry}}. Note that {{define|mirror symmetry}} is just another word for reflection symmetry. You can use either one of these terms. The line is known by several different names. Sometimes it's called the {{define|reflection line}}, others may call it the {{define|mirror line}}, or the {{define|axis of symmetry}}.
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The important part to remember is that this line separates the figure into two parts, one of which is a mirror image of the other part.
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Here are several more examples of this mirror symmetry:
  
 
[[Image:bilateral.svg|center]]
 
[[Image:bilateral.svg|center]]
  
The heart and smiley each have a vertical axis of symmetry, and the lobster has a horizontal axis of symmetry.  The arrow has an axis of symmetry at an angle.  If you draw the reflection line though any one of these figures, you will notice that for every point on one side of the line there is a corresponding point on the other side of the line.  If you connect any two corresponding points with a segment, that segment will be perpendicular to the axis of symmetry and bisected by it (cut into two equal length segments):
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The heart and smiley each have a vertical mirror line, and the lobster has a horizontal mirror line.  The arrow has a mirror line at an angle.  If you draw the mirror line though any one of these figures, you will notice that for every point on one side of the line there is a corresponding point on the other side of the line.  If you connect any two corresponding points with a segment, that segment will be perpendicular to the axis of symmetry and bisected by it (cut into two equal length segments):
  
 
[[Image:heart-symmetry.svg|center]]
 
[[Image:heart-symmetry.svg|center]]
  
Bilateral symmetry is the most common type of symmetry found in nature, occurring in almost all animals and many plants.  Congnitive research has shown that the human mind is specially equipped to detect bilateral symmetry
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Mirror or reflection symmetry is the most common type of symmetry found in nature, occurring in almost all animals and many plants.  Scientists have shown that our brain is rather good at recognizing this type of symmetry.
 
[http://www.nici.kun.nl/~peterh/doc/goodness.html].
 
[http://www.nici.kun.nl/~peterh/doc/goodness.html].
In fact, humans are especially good at detecting bilateral symmetry when the axis of symmetry is oriented vertically.  As you proceed through this course, you will look for symmetry in all sorts of complicated images.  Remember that your eyes are hard wired to do this well when the axis is vertical, and so it will be a tremendous help to rotate the images (or your head) as you look for symmetries.
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In fact, people are especially good at detecting mirror symmetry when the mirror line is oriented vertically (up-down).  As you proceed through this course, you will look for symmetry in all sorts of complicated images.  Remember that your eyes are hard wired to do this well when the axis is vertical, and so it will be a big help to turn the images (or your head) as you look for symmetries.
  
Some objects or images can have more than one axis of reflection symmetry.  Here are some examples, with the reflection axes shown as dotted red lines:
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Some objects or images can have more than one mirror line.  Here are some examples, with the mirror lines shown as dotted red lines:
  
 
[[Image:reflection-symmetries.svg|center]]
 
[[Image:reflection-symmetries.svg|center]]
  
Pay special attention to the diagonal reflection axes in the cross.  These are easy to overlook, and occur frequently.
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Pay special attention to the diagonal reflection axes in the cross.  These are easy to miss, and do show up quite often.

Revision as of 10:43, 23 February 2009

K-12: Materials at high school level.


If one side of the image is the mirror image of the other side, then we say the figure has reflectional symmetry. Sometimes we would say that the image has a mirror line. Here we have some images from real life that have such mirror lines. The image on the left is McCarren Park Pool in New York. The red line in the center was added to show you where the mirror line is located. The next image is a piece of a Persian rug. Here again you can see that the left side is an exact mirror image of the right hand side. The bug right next to it also has a vertical mirror line, and the left side is a mirror image of the right side. The image of the ducks shows that the mirror line can also run in other directions. In the duck picture the mirror line runs from left to right.

McCarren-Park-Pool.jpg Farsh1.jpg Aragaru1.JPG Whistling-Duck.jpg
McCarren Park Pool A rug A Beetle Ducks


To make the idea of symmetry a bit more precise, we would say that if points of a figure are equally positioned about a line, then the figure has reflection symmetry. Note that mirror symmetry is just another word for reflection symmetry. You can use either one of these terms. The line is known by several different names. Sometimes it's called the reflection line, others may call it the mirror line, or the axis of symmetry. The important part to remember is that this line separates the figure into two parts, one of which is a mirror image of the other part.

Here are several more examples of this mirror symmetry:

Bilateral.svg

The heart and smiley each have a vertical mirror line, and the lobster has a horizontal mirror line. The arrow has a mirror line at an angle. If you draw the mirror line though any one of these figures, you will notice that for every point on one side of the line there is a corresponding point on the other side of the line. If you connect any two corresponding points with a segment, that segment will be perpendicular to the axis of symmetry and bisected by it (cut into two equal length segments):

Heart-symmetry.svg

Mirror or reflection symmetry is the most common type of symmetry found in nature, occurring in almost all animals and many plants. Scientists have shown that our brain is rather good at recognizing this type of symmetry. [1]. In fact, people are especially good at detecting mirror symmetry when the mirror line is oriented vertically (up-down). As you proceed through this course, you will look for symmetry in all sorts of complicated images. Remember that your eyes are hard wired to do this well when the axis is vertical, and so it will be a big help to turn the images (or your head) as you look for symmetries.

Some objects or images can have more than one mirror line. Here are some examples, with the mirror lines shown as dotted red lines:

Reflection-symmetries.svg

Pay special attention to the diagonal reflection axes in the cross. These are easy to miss, and do show up quite often.