SYMMETRY:Ideas for Exercises for the K-12

Classroom

Part II: Rotation and Reflection Symmetries in Letters, Words, and Sentences

C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

SymmetrySymmetry

Examine the capital letters of the Latin alphabet.

Identify the mirror planes and rotation axes of each letter.

Notice that some letters might have symmetry depending on how they are written.

-- Arial normal font is a good font for demonstrating symmetry.

-- Serifs destroy the symmetry of many letters

How does the symmetry of the lower-case letters compare to that of the upper-case letters?

A B C D E F G H I

J K L M N O P Q R

S T U V W X Y Z

a b c d e f g h i j k l m n o

p q r s t u v w x y z

The Latin Alphabet

C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

SymmetrySymmetry

Examine the letters of other alphabets, such as the Greek alphabet.

Identify the mirror planes and rotation axes of each letter.

Consider how serifs remove symmetry in some cases.

Consider how the font style affects the symmetry in some cases

The Greek Alphabet

C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

SymmetrySymmetry

Words can have symmetry

1. If it’s only in the order of the letters, then it’s a palindrome (the same forward and

backward):

ANNA, BOB

2. However, some words have true symmetry elements:

OTTO, MOM, CHECKBOOK, bid

For fun, names with symmetrical orders of the letters can be rewritten so that they contain true

symmetry elements:

BOB BOB or BOB

What are some other examples of symmetrical words?

Symmetry in Words

C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

SymmetrySymmetry

Sentences with symmetry are also known as palindromes.

Dee saw a seed.

Is it I? It is I!

Was it a bar or a bat I saw? What are some other examples of symmetrical words?

Symmetry in Sentences

C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

SymmetrySymmetryReferences and Related Topics

1. http://www.fun-with-words.com/word_records.html, accessed on 1/20/2014

2. http://www.palindromelist.net/, accessed on 1/23/2014

3. http://www.merriam-webster.com/dictionary/palindrome, accessed on 1/23/2014

4. Ambigrams, for example:

1. http://www.hongkiat.com/blog/creative-and-cool-ambigram-designs/

2. http://vector.tutsplus.com/articles/inspiration/a-clever-collection-of-40-inspiring-

ambigrams/

5. Interesting examples of symmetry

1. http://www.xtal.iqfr.csic.es/Cristalografia/parte_03-en.html

C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org