Point and Line Symmetry in the AlphabetDate: 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/ |
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