Point and Line Symmetry in the Alphabet

Date: 12/05/97 at 23:27:19
From: Nancy Montone
Subject: Point and line symmetry in the alphabet

The question was to examine the letters of the alphabet to determine 
which ones have point symmetry, line symmetry, or both.  How many 
letters have neither form of symmetry?

I understand the idea of line symmetry and have identified the letters 
A,B,C,D,E,H,I,M,O,T,U,V,W,X, and Y as having line symmetry.  

If I understand point symmetry correctly then O and possibly X are the 
only letters that have both point and line symmetry. This would leave 
F,G,J,K,L,N,P,Q,R,S,and Z, for a total of 11 letters, that have 
neither point nor line symmetry. Am I correct?

Date: 12/08/97 at 12:40:36
From: Doctor Tom
Subject: Re: Point and line symmetry in the alphabet

Hi Nancy,

There are some letters that have point symmetry and not line symmetry:  
N, S, and Z. Consider the point in the center of each of those letters 
- halfway down the diagonal lines of the N and Z, and right where the 
S starts to curve the other way. You can reflect any point on those 
letters through that center point, and be back on the letter.

In addition to O and X that have both point and line symmetry, the 
letters H and I also have both forms. In fact, you will note that the 
letters that have both point and line symmetry actually have two lines 
of symmetry - in this case both a horizontal and vertical line passing 
through the center of the letter. It turns out that any figure with 
two different lines of symmetry will also have point symmetry.

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/