Jordan Massoud- Blog #3: Mathematical concepts in "Go, Dog. Go!"

I read the book, "Go, Dog. Go!" written and illustrated by P.D. Eastman in 1961. The short children's book chronicles the life of a group of dogs commingling throughout the span of two days. “Go, Dog, Go!" seems to be written from the perspective of a third person observer that is traveling throughout the dogs' town watching their various interactions. Being a fairly short, nonsensical book, the summary may seem a bit illogical and jumpy. Nevertheless, the book begins with a comparison of the sizes of dogs and their colors- big and small, black and white. We are then introduced to two dogs lounging on tree: a red dog on a blue tree and a blue dog on a red tree. Moving forward, we see what the dogs do for fun. There are dogs going up a roller coaster and a different dog coming down the roller coaster. There are dogs playing in water, with one jumping off a diving board, some swimming under water, and a grumpy neighbor peering on. As the first night approaches, three dogs are still sailing in the water, playing chess. But, as day comes, the dogs work their construction jobs, but play baseball after. The second night comes and we see all the aforementioned dogs sleeping in one giant bed together. Eventually, morning comes and the dogs race in their cars toward a big tree where there's a huge party taking place. They continue to party as the sun sets, and the book awkwardly comes to a close.

Short of sounding like the ravings of an insane person, "Go, Dog. Go!" presents multiple mathematical concepts: linear equations, slope of the line, inverse relationships, and the properties of a parabola. Firstly, "Go, Dog. Go!" illustrates an easy example of inverse relationships by comparing a big dog and little dog, and a black dog and white dog, and a red dog sitting on a blue tree with a blue dog sitting on a red tree. These contrary comparisons, although a bit odd, do represent a similar idea to inverse relationships in math: 1/3 equals 3/1 or 3. 

A more major mathematical representation can be seen in the scene where two big dogs are shown going up a roller coaster, while one small dog comes down it. The shape of the roller coaster is identical to the shape of the parabolas we studied in class. The general formula for a parabola/quadratic function is: f(x)= ax^2+bx+c, where a, b, c are all constants. However, the graph of this formula is concave up, while the shape of the roller coaster is concave down. Thus, the hypothetical graph of the roller coaster might look like: f(x)= -ax^2+bx+c. That way, the roller coaster has a maximum height, symbolizing the point where the graph stops increasing and starts decreasing.

Another mathematical concept presented in "Go, Dog. Go!" is that of a linear equation. This concept surfaces itself twice in the same scene. First, the reader sees a straight line of cars racing towards the big tree. Then we see the dogs climbing a ladder leaned up against the big tree. These two images illustrate the concept of linear equations and rate of change. The dogs racing toward the big tree form a perfectly straight and can be modeled by a linear equation. Additionally, the ladder leaning against the big tree also illustrated a linear model. In general, a linear function is one where the rate of change at every interval is the same and the graph results in a straight line. In terms of the dogs racing in cars toward the tree and the ladder leaned up against the tree, the slope of those lines are constant throughout, which is evidenced by the straight lines those images form.

Literature can be extremely beneficial in learning mathematical concepts. Since many people learn better in terms of written words or images, rather than equations or formulas, literature offers an accessible medium through which readers can connect with math concepts. Additionally, by using real-life scenarios, it again makes the concepts more digestible to the average reader. For example, everyone can relate to riding a roller coaster, but if you ask someone to explain the concepts of concavity, increasing/decreasing functions, or  maximum/minimum values they will probably struggle. In conclusion, I feel literature, especially children's books, provide a valuable service to society by simplifying math concepts and putting them into terms everyone can identify with.