Plane Symmetry

Date: 10/3/95 at 17:28:29
From: Anonymous
Subject: plane symmetry

I am a first year b.ed. student and have to do a mathematics paper 
on plane symmetry and also a challenging activity related to this.  
The activity has to be appropriate for grades four to six.  I have 
checked a lot of mathematics texts, but they fail to give me an 
in-depth understanding of this topic.  Can you suggest a possible 
resource I could use, or do you have any suggestions for me?  I 
would appreciate any help you can give me.  Thanks.

Date: 10/9/95 at 20:31:6
From: Doctor Jonathan
Subject: Re: plane symmetry

Plane symmetry is analogous to line symmetry, except in three 
dimensions.  For example, if the graph of an equation 
f(x,y,z)=g(x,y,z) has plane symmetry about the x-y plane, then the 
point (x,y,z) satisfies the equation if and only if (x,y,-z) does 
as well.  As for a good way to illustrate this to students, you 
might want to use a mirror (which would be the plane of symmetry) 
and some simple objects. The image they see "through" the mirror 
has plane symmetry. You might want to ask the kids if they can 
think of everyday objects that exhibit plane symmetry and see if 
they can say where the reflecting plane is in each object. Some 
common objects with plane symmetry: spheres, boxes, swords, planes 
(that fly), humans (sort of).  If the kids really aren't 
nterested, you could mention that handguns, swords and bombs have 
plane symmetry. You might ask them: How many planes of symmetry 
does a cube have? A sphere?

Hope this helps.

-Doctor Jonathan,  The Geometry Forum