Difference between revisions of "Symmetry"

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The term Symmetry arises in a number of contexts, and has several, related meanings<ref> Intial definitions from: http://www.m-w.com/dictionary/symmetry</ref> :
 
The term Symmetry arises in a number of contexts, and has several, related meanings<ref> Intial definitions from: http://www.m-w.com/dictionary/symmetry</ref> :
 
   
 
   
* It may refer to an object which has balanced proportions, and the beauty of form arising from those balanced proportions, notably a face, or an animal, e.g a racehorse.
+
* It may refer to an object which has balanced proportions, and the beauty of form arising from those balanced proportions, notably a face, or an animal, e.g a tiger, as in Blake's poem:
 +
TIGER, tiger, burning bright 
 +
In the forests of the night, 
 +
What immortal hand or eye 
 +
Could frame thy fearful symmetry?
 +
 
 
* It may refer to the property of being mathematically symmetrical, especially relating to a correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis; sometimes the term [[bilateral symmetry]] is used in this context.  
 
* It may refer to the property of being mathematically symmetrical, especially relating to a correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis; sometimes the term [[bilateral symmetry]] is used in this context.  
 
* It may refer to an [[isometry|isometric transformation]] or [[rigid body motion]] of a geometric figure, which determines a one-to-one mapping onto itself, and which preserves angles and distances. There are four such kinds of [[isomorphism]]:[[Rotation]]s, [[Reflection]]s, [[Translation]]s and [[Glide-Reflection]]s
 
* It may refer to an [[isometry|isometric transformation]] or [[rigid body motion]] of a geometric figure, which determines a one-to-one mapping onto itself, and which preserves angles and distances. There are four such kinds of [[isomorphism]]:[[Rotation]]s, [[Reflection]]s, [[Translation]]s and [[Glide-Reflection]]s

Revision as of 06:56, 14 May 2007

The term Symmetry arises in a number of contexts, and has several, related meanings[1] :

  • It may refer to an object which has balanced proportions, and the beauty of form arising from those balanced proportions, notably a face, or an animal, e.g a tiger, as in Blake's poem:
TIGER, tiger, burning bright   
In the forests of the night,   
What immortal hand or eye   
Could frame thy fearful symmetry? 
  • It may refer to the property of being mathematically symmetrical, especially relating to a correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis; sometimes the term bilateral symmetry is used in this context.
  • It may refer to an isometric transformation or rigid body motion of a geometric figure, which determines a one-to-one mapping onto itself, and which preserves angles and distances. There are four such kinds of isomorphism:Rotations, Reflections, Translations and Glide-Reflections
  • It may also refer to the property of remaining invariant under certain changes (as of orientation in space, of the sign of the electric charge, of parity, or of the direction of time flow) -- used of physical phenomena and of equations describing them.

References

  1. Intial definitions from: http://www.m-w.com/dictionary/symmetry