SYMMETRY Ideas for Exercises for the K12 Classroom

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

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

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

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 or BOB § What are some other examples of symmetrical words? C. Y. Jones, Columbia University, January 2014, www. solidstatechemistry. org

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

Symmetry References 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 -inspiringambigrams/ 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