How Mathematics and Art Are Interconnected. Liz Sweetwood. October 24th, 2016

Transcription

1 How Mathematics and Art Are Interconnected Liz Sweetwood October 24th, 2016

2 2 Throughout time, Art has been an outlet for a creator to openly express themselves and the way they see the world around them. In order to create a masterpiece, the craftsman uses Mathematical thinking when developing an idea, by sketching or outlining what they intend to create. The author Doris Schattschneider a professor at the Moravian College supports that thought in her statement In the hands of an artist, mathematically-produced art is only a beginning, a skeleton or a template to which the artist brings imagination, training, and a personal vision. (Schattschneider 2013). Again it establishes that Art and Math both use imagination and thought as a basis for creativity to happen. Some examples of Art seen in daily life can include scenic photos while traveling, children s drawings, album covers to a band, and the the bright clearance signs seen while shopping. Nonetheless, Math also shows up often in our day to day activities. For example Math is used while tipping at a restaurant, calculating sale percentages, making a monthly budget or even measurements for recipes. A blog written by Joseph Malkevitch a professor at York College is in favor of the proposition that Art and Math are related. He provides examples in history to prove his theory,...some mathematicians have become artists, often while pursuing their mathematics. Among such artists were Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, and M.C. Escher. (Malkevitch 2016). This particular essay will be establishing a link between the subjects of Math and Art, by giving the topic examples of shapes, symmetry, and motifs. The first topic of correlation is how Mathematical objects such as Geometric and Organic shapes, are also used in producing items in Art. Geometric shapes have clear definite edges such as triangles, rectangles and stars. And Organic shapes have less defined edges that more curvy and contoured like as clouds, leaves and swirls. Also certain objects in Art can be often

3 3 associated with specific ideas or thoughts. For example, a heart on an image may symbolize love or embellishments on a dress may express luxury and wealth. Any creation of Art goes through stages, the first part of that process is planning out what the piece will look like and include, then the Artist begins to use simple shapes to bring their imagination to life. Think of an illustrator that creates Children's picture books, he needs to create a pumpkin image because the book is about Autumn. So first the author could sketch a circular oblong shape for the pumpkin with a vertical rectangle at the top for the stem. And later the illustrator could go back and make the outline less defined so it appears more like a natural pumpkin. Likewise in the context of Math, not all number systems through history have used the numbers zero through nine, liked used in present times. The ancient Mayans and Egyptians are just a couple instances where their number systems contained objects or common shapes, instead of formal numbers. The writer Mikelle Mercer describes the Mayan number system structure as having two important markers in this system are 20, which relates to the fingers and toes, and five, which relates to the number of digits on one hand or foot. The Mayan system used a combination of two symbols. A dot (.) was used to represent the units (one through four) and a dash (-) was used to represent five. (Mercer 2000). Similarly another author named Lloyd Holt commented on the Egyptian numeral system stating that hieroglyphic numeration was a written version of a concrete counting system using material objects. To represent a number, the sign for each decimal order was repeated as many times as necessary. To make it easier to read the repeated signs they were placed in groups of two, three, or four and arranged vertically. (Holt 2000). Ordinary found shapes have been used for centuries in Math and also in Art to convey certain characteristics. Professor Carla Farsi of Colorado agrees by saying numbers and mathematics are intrinsically present in natural objects,

4 4 and both artists and mathematicians have used these ideas in their respective disciplines. (Farsi p13). In Math, objects were used in place of a counting system, and in Art certain shapes and symbols revealed specific attitudes and or feelings the author is showing through that piece. The next way Art and Math are associated is through symmetry. Symmetry also has multiple forms, some common ones are rotational symmetry and point symmetry. Rotational symmetry is when an object is rotated but it still has the same formation. And Point symmetry is when each part of an image has a corresponding part and the parts are facing in the opposite direction. Symmetry in exists in Art because it s appealing to the eye and it has balance within itself. Symmetry is enjoyable because human bodies are symmetrical so than people can feel the relation to the work of art. Most individuals have two eyes, two ears to hear on both the left and right side, and lastly two legs to walk and balance on. Symmetry in Math is used for solving system of equations and solving for variables. The quote what you do to one side of the problem, do to the other is common because it reminds a person to keep numbers symmetrical and balanced. The author Alexander Voloshinov wrote about the significance of balance, important principle of harmony both in the universe and in art. The idea of symmetry as the means to perfection, led Pythagoras to the correct hypothesis about the spherical shape of the Earth and the circularity of planetary orbits. (Voloshinov p109). So thus not only is symmetry found in Art, but it also helped Mathematicians centuries ago solve theories about the world. Symmetry in Math is still used today to balance checkbooks and in Art such as make overs on half of a person s face to show the difference. Schattschneider lists examples of how symmetry is used in both subjects "proportions have always been fundamental in the aesthetic of art, guiding composition, design, and form. Mathematically, this translates into the observance of ratios.

5 5 Whether these be canons of human proportion, architectural design, or even symbols and letter fonts, ratios connect parts of a design to the whole, and to each other. (Schattschneider 2003). And lastly, Motifs are paired with Math and Art because they both use a pattern to achieve their goal. In Art, Motifs are a decorative design such as Paisley Doleys on t-shirts or a Celtic knot motif on a family shield. Motifs can be either natural or simulated, an organic item is naturally occurring for example wild flowers. And something simulated is made up of certain traits to get a desired effect for instance, crossbreeding traits in a crop to get bigger production and so the crop can be drought tolerable. In Math there are patterns like Motifs that help solve problems and find different place values, they re known as formulas and or theorems. Formulas come up in the many different math topics such as Algebra, Geometry, and Statistics. A formula uses symbols to express a relationship or to help solve for an unknown. One common math pattern is the acronym PEMDAS. PEMDAS stands for parenthesis, exponents, multiplication, division, addition and subtraction. People can use that acronym pattern to help remember what order to do an equation in. Schattschneider included the statement that a pattern is a fundamental concept in both mathematics and art. Mathematical patterns can generate artistic patterns. (Schattschneider 2003). So once more like a repeated and designed Motif in Art, formulas can also be used and repeated in many different instances to eventually create some form of craft. Farsi also supports that in her quote Mathematics can indeed be defined as the general science of pattern and structure. Because art also involves patterns and structures, art and math relate to each other in many natural ways. (Farsi 2005).

6 6 One might ask how could Math and Art ever be related? Math seems to be more methodical and Art seems to be more about creativity. But actually both elements include methodical thinking and creativity to produce some type of elegant end result. So within this text it has in demonstrated how Art and Math are related by listing three different instances. And those three different topics were shapes, symmetry, and motifs. It is a such a growing phenomenon that a group of Scientists, Artists, and Math professionals banded together to create an organization called The Bridges. By working together at the University of Colorado the organization displays exhibits that have Mathematical Art. Farsi wrote a great statement saying that, Art and mathematics is their deeper purpose to reveal truth about our world and ourselves. Both disciplines strive to discover and represent the unknown. (Farsi p12). Yet again Math and Art are affiliated because they have a deeper purpose, a person isn t just solving a for x variable or just drawing a picture. But instead they use both features of Math and Art in order to find a deeper meaning in life, and to fulfill their visions for the future.

7 7 Works Cited : Farsi, Carla, and Doug Craft. One in Two, Two in One: Mathematics and the Arts. Math Horizons, vol. 12, no. 3, 2005, pp Malkevitch, Joseph. "Mathematics and Art." American Mathematical Society. N.p., 12 June Web. 25 Oct < Mercer, Mickelle, and Luke Holt. "Number Systems." Number Systems. N.p., 7 Feb Web. 25 Oct < >. Schattschneider, Doris. "Mathematics and Art - So Many Connections." MAM2003 Essay. N.p., Apr Web. 25 Oct < >. Voloshinov, Alexander V. Symmetry as a Super Principle of Science and Art. Leonardo, vol. 29, no. 2, 1996, pp