Exploring Symmetry in Alphabets & Sentences

1. 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

2. Symmetry The Latin Alphabet • 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 C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

3. Symmetry The Greek Alphabet • 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 A B G D E Z H Q I K L M N X O P R S T U F C Y W a b g d e z h q i k l m n x o p r s t u j v f c y w C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

4. Symmetry Symmetry in Words • 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? C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

5. Symmetry Symmetry in Sentences • 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? C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org

6. Symmetry References and Related Topics • http://www.fun-with-words.com/word_records.html, accessed on 1/20/2014 • http://www.palindromelist.net/, accessed on 1/23/2014 • http://www.merriam-webster.com/dictionary/palindrome, accessed on 1/23/2014 • Ambigrams, for example: • http://www.hongkiat.com/blog/creative-and-cool-ambigram-designs/ • http://vector.tutsplus.com/articles/inspiration/a-clever-collection-of-40-inspiring-ambigrams/ • Interesting examples of symmetry • http://www.xtal.iqfr.csic.es/Cristalografia/parte_03-en.html C. Y. Jones, Columbia University, January 2014, www.solidstatechemistry.org