Calise's Pieces

Introduction:

What do the subjects German, mathematics, religion and art all have in common? I could tell you, but it would take 23 years to explain. Art and mathematics however are a bit easier to relate, believe it or not, and that is what we will be doing in this paper. When I introduced myself as an art major at the beginning of this semester, I felt the looks of slight confusion and concern. I am not surprised if this paper attracts similar reactions, but hopefully we can ease those concerns and shed some light on the subject, and maybe even encourage some of you mathematicians, to use some color next time you write formula.

The statue of David is one of the most well-known pieces of art in the world. Famous for the artist who carved it, the size it was finished at, and the story behind it. One thing most people don't know without studying it, is how disproportionate Michelangelo made this great statue. To the untrained eye, the typical tourist might see the man's figure and think it looks quite realistic, shocking, and quite beautiful, But for the artist, or for someone who will look more critically at the work, they will see that Michelangelo made some features, such as the eyes, chest and hands of the figure, slightly larger than anatomically correct, as to draw attention and focus to these parts, thus complimenting and strengthening the ideas and meaning behind the piece. (McCulloch, 2007)

The Math:

What does this have to do with mathematics you might still be asking? Michelangelo was not only an artist, but he was highly aware of the mathematics which were to be considered in making this, and any work of art, in this case, one example is the power of proportions. Leonardo Da Vinci was another great historical figure, called a scientist, mathematician, and yes, even an artist. His drawing and study of the Vitruvian Man, also known as "The proportions of the human body according to Vitruvius," is often used as a reference for health and medical imagery, but while there are obvious aspects that can be honored and praised for their artistic characters, he wasn't just making art here.

"The Vitruvian Man is based on De Architectura, a building guide written by Roman architect and engineer Vitruvius between 30 and 15 BC. While it is focused on architecture, the treatise also explores the human body-namely, the geometry of "perfect' proportions-which appealed to Leonardo's interest in anatomy and inspired his drawing." (Richman-Abdou , 2018) The text surrounding the image state some of his findings and calculations such as, "From the bottom of the chin to the top of his head is one eighth of his height... From the top of the breast to the top of his head will be one sixth of a man... The foot is the seventh part of the man..." (Richman-Abdou , 2018).

With these calculations in mind, there is now a clear correlation between anatomy and mathematics, as Da Vinci pulled the numbers out of the image, but how does this relate to teaching mathematics? Well, for one idea, I can recall learning some of these calculations as a child in one of my favorite animated cartoons called Cyberchase, where a lot of the missions and assignments given to these kids, involved more than just seeing and understanding the numbers, but rather, was about being able to see a problem and use found objects, past lessons and tools to bring the numbers to life, and ultimately find a solution.

In one episode, the kids' only clue in trying to find a thief, is a footprint the thief left behind in the mud. Through the episode the kids try to find "body matches" or connecting parts of the anatomy on themselves, to try to calculate the proportions of the thief. By the end of the show, they have compiled enough calculations to build a rough model, and save the day. Although this show is meant for kids grades 3-5, what this episode was showing, was many of the same calculations that Vitruvian and Da Vinci were studying. Although they were found and taught in a more playful manner, the number and the technique are the same.

From these examples alone we could also examine many other topics such as symmetry, comparison, shape or lines, all of which are both mathematic and artistic properties.

Why connect art to math?

In just these three displays of the human figure, we have already seen that there is a great connection between art and math. Art without mathematics would be less correct, more abstract, and likely less successful altogether. What about mathematics without visuals?

Take integrals and derivatives for example. The equation "d/dx sin(x) = cos(x)," is one that is simple enough to the student trained in calculous, but how is that to be explained to someone less familiar with functions and arithmetic? One way to show this equation, is with the graph, and drawing it out to show that a derivative of a function, can also be referred to as the rate of change or the slope of a function. With the visual of the graph, equations such as "d/dx * 2 = 2x" become more than just easier to wrap your head around, but it also become easier to relate to. A student could connect this to speed and acceleration in science, they could then draw connections to other greater mathematic concepts, or this little glimpse of understanding could simply do the good of boosting the confidence of this student in mathematics altogether.

Not every student aspires to be a great mathematician or scientist, but every student will face the potential of becoming an adult, and a lifelong problem solver, because regardless of who we are or why we are somewhere, we will constantly be faced with choices and decisions. It is our education and understanding that will be our greatest tools in this life, and if art does anything, it bridges the gap between ideas and expression.

Just as we don't have classes specifically for creativity or understanding, some topics are best taught by being woven into lessons of varying subjects. In history we learn of innovation and invention of people who were trying to prove the impossible, or simply trying to overcome a barrier or challenge, well, these are the lessons that will get us all through life, whether we learn to fly like the Wright brothers, or we simply learn how to communicate and compromise with those we live with. This is what art has become for me, not only a medium which I can use to create fun projects and express emotions and ideas, but also as a platform for me to learn to problem solve, visualize and break things down to the sketch that will hopefully lead to the great sculpture I hope to complete.

Implementing art into mathematic teaching:

It doesn't take stone carving to make math more artistic, some ways to include more art into mathematics can be as simple as using graphs and figures as was stated to above. The simple use of a graphing calculator pulled me though many tests and lessons as I was able to see how the numbers linked and grew into curves, shapes and relationships. According to Melissa Kelly, with visual learners, it is useful to "Include diagrams, mind maps, word webs, visuals and other forms of graphic organizers to help visual learners get the most from your instruction."

Other ideas can be as creative as asking the class to build a cube out of toothpicks and marshmallows, and asking them to take it apart to see how the cube is really constructed. When possible, I have found though experience that getting my hands on tools, and building and breaking things down can be extremely helpful in understanding. Erica, on her website "what we do all day," has listed several math-art projects that are fun for kids, and still informative, including this Fibonacci project with paper and a compass.

Applets are also great tools in introducing the reality and effect of the numbers and variables on different functions. For example, on the website Math is Fun, there are animated shapes and objects, that can be viewed as the 3D object, the net, or flat arrangement of the planes, be rotated, or seen as an "exploded" version, where each plane is spaced, allowing the student to see the basic shapes that make up the greater object. Tools like this are useful in cases where limitations of in person examples are restricted, where the student may have physical or other disabilities that restrict them from drawing or comprehending a 3D object in a 2D space, or even in situations of large classes this would allow students a freedom to discover new things for themselves, and find questions and solutions on their own.

Conclusion:

One of our goals as educators is to expand the mind of the students and help them understand new concepts. One of the greatest thing I learned, through a childhood TV shows, and throughout my education, was that there are many ways to solve one problem. You don’t have to be a great scientist to learn that some measurements can be combined and correlated to prove greater equations, or even that some concepts or lessons can apply to a broad range of situations and topics.

Art is more than just colors and shapes. Art is meaning and feeling, beauty and history, and so much. Just as math is more than just numbers and equations, it can be bridges and buildings, curves and globes, even history. The truth is, art needs math and math needs the arts. Some people can sit in front of a painting by Georges Seurat for hours and dissect and learn from his dots and colors, figures and shapes, while another can be as equally fascinated with the Pythagorean theorem, Pi, or other ground breaking calculations that have changed the world.

I am lucky to have the perspective to be able to see both of these, the beauty in the numbers, as well as the rhythm and science in the art, and that is why I want to be a teacher, and why one of my main goals and focuses as an aspiring educator, is to help other see the connection in all things. I happen to love math and art, but through these two things, I have come to realize that there is a way to use any interest, to improve the understanding of another.

"The basic idea is that all things in the universe are intertwined." - Stephen Richards