Ideas for Exercises for the K-12 Classroom

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Presentation transcript:

Ideas for Exercises for the K-12 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 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

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

Symmetry Symmetry in Words BOB BOB or BOB 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

Symmetry Symmetry in Sentences Dee saw a seed. Is it I? It is I! 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 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