Chapter 15: Rotations and Reflections

    In Chapter 15 of “ The Colossal Book of Mathematics,” Martin Garden introduces the topic of rotations and reflections. The chapter brings up many examples of symmetry found in nature and how artists utilize different types of symmetry in order to create fascinating illusions. Thus, the readers are able to explore various cases of mathematical art in their daily lives.

    The chapter starts of by explaining that “[a] geometric figure is said to be symmetrical if it remains unchanged after a “symmetry operation” has been performed on it” (Gardner, 189). Also, the more operations you can perform of the figure, the “richer” it is. For example, the letter O is the richest out of all the other letters because it is unchanged by any type of rotation or reflection. Many artists from the late 19th to the mid 20th century have applied this technique to their artworks. Political cartoonist would draw famous public figures, and when the reader would invert the picture, they would see a pig or a donkey or something equally offensive. This device of upside-down drawing was taken to further heights by the cartoonist Gustave Verbeek. He worked for the New York Herald, and every Sunday he would draw a six panel comic strip. In order to read it, one first reads the newspaper right side up and then to continue the story, the paper must be flipped over, which held a new set of captions and took the same six panels in reverse order.

    Types of rotations cause also cause optical illusions. For instance, astronomers view photographs of the moon’s surface so that the light appears to illuminate the craters from above because if it was inverted or below, the craters would look like mesas jutting out of the surface. A very amusing illusion is that of a circular pie with a slice missing. If you were to turn the picture upside-down, one can find the missing slice. This shows how one is used to seeing things, like plates and pies, from above and not below.

    From the article “The Doodle Bug,” by Emily Bearn, she explains the type of rotational art called ambigrams. An ambigram is a word or art form whose elements retain the same meaning when viewed from a different direction or perspective. I wish the author would’ve included this small topic into the chapter because it is a very intriguing aspect of rotations and reflections in order to create art. The chapter is already short as it is, so it would’ve benefited by adding this into it. However, I’m glad Martin Gardner omitted going into detail about the lives of the artists he talked about. Bearn dives into the life of John Langdon, a professional in ambigrams. If he were to include the specifics of some people’s lives, it would’ve taken away from the main position of the chapter.

    In the article “Group Think,” the writer Steven Strogatz brings up an important topic, group theory. He explains how “group theory bridges the arts and sciences. It addresses something the two cultures share - an abiding fascination with symmetry.” Strogatz shows a practical usage of rotations and reflections in our daily lives, which is something Gardner didn’t cover, but should have. In his article, he explains how you can rotate a mattress three different ways in order to make it last longer. You can either flip it horizontally, vertically, or rotate 180 degrees. However, I’m glad that Gardner didn’t put in equations of rotations and reflections in his chapter. I believe it would’ve confused the readers and be redundant as the pictures already provide enough explanation.

    In my final reference, “The Turn About, Think About, Look About Book,” by Beau Gardner, it gives many pictures of the topics covered in the chapter. The book is made like a children’s book, so anyone can read it and enjoy it. What I think Martin Gardner should’ve included was more pictures of rotations and reflections because readers would’ve been entertained trying to solve what the illusion is. What I’m glad that Martin did omit was the childish aspect that’s from the “The Turn About, Think About, Look About Book.” His chapter gives more of an intellectual look than what Beau Gardner provides.

    This chapter was stimulating and very simple. It is one of the more easy to follow chapters in the book compared to other concepts. Also, it is a refresher from all the numbers and equations math is known to throw at you.