Mathematics and Poetry

Math G KimLy

Final Paper 11/25/02

Mathematicsand Poetry

"Mathematics speaks to the mind, poetry to theheart". (http://www.kavitanjali.com/pgmarch02/onpoetry.htm), Finding the link between mathematics and poetry is a challenge. Thereason for this is the fact that mathematics deals with reasoning, calculating,proving, and then resulting in one final answer; whereas poetry deals withrhymes, feelings, symmetry, and poetry always offers more than onesolution. However, with the introductory quote above, a very interestinglink can be drawn to connect two very extreme studies to be relatedtogether. This connection is made taking humans as a link between thetwo. That is, we use our mind to do mathematic calculations, we use ourheart to express thoughts or feelings through poetry, and since our heart andmind are connected to each other, there should be a way to link mathematics andpoetry together. Thus, with this research paper, I would like to godeeper into how poets and mathematicians were able to integrate the two studiestogether.

Math was not my favorite subject and poetry has alwaysaroused interest in me. Ever sinceI take this Math G course as a liberal art class, I find that learning mathdoes not have to be tied down with only calculations and intense problemsolving. It can also be learnedwith a liberal art perspective.

From saying this, I decide to combine what I like alot to something I don't really like and see how well one subject leads to abetter understanding of another subject.

The poem below titled "Algebra One" writtenby poet Daphne N., Needham, MA, expressed how simple algebra can be. It lists out the general terms,formulas, and concepts that algebra has. In addition, it has a tone of humor in the poem. What I especially like is thesimilarity that exists between the poet and me. Because, just like myself, I had a hard time with math; Ialways get confused by looking at numbers and equations, but when I read thispoem, I was able to get a very good overview of what algebra is about. The overview is explained in a verypoetic way, which interests me very much.

"Remember all thoserationals and irrationals, the ones we got confused?

I still get them wrong and Iam not very amused.

Digits and decimals, too manyD's

But wait until we start onthose x,y, and z's.

Powers of 10 are expressed byexponents in many ways,

But, remember, there is onlyone and that is to have them raised.

Counting all those zerosmakes me very crazy,

So use that scientificnotation and don't be so lazy.

Collections of elements insets are a breeze.

Elements follow a patternjust like 1,2, and 3's.

A variable is a symbol like xwhich has 1 value, not 2.

If you put the right variablein an open sentence, the statement will be true.

Factoring numbers can be sucha bore!

But, prime numbers are thebest since the factors are only 1 and itself, and nothing more.

Basic axioms of algebra leaveyou in awe,

But not to understand them isone major flaw.

The most important axiom isthe distributive one.

It's the one we used themost, but it wasn't that fun.

Reciprocals are the numbersthat always do a flip upside down.

Inverses are very differentand in their own special way turn around.

Numbers are variables arejumbled disorderly,

Are called equations and areonly solved algebraically

Solving inequalities can makeyou want to die,

But, there are only 3choices: greater than, less than,or equal to, so there is no need to cry.

Polynomials can leave you insuch a disarray,

But, just remember there arecoefficients and constant terms and then you will be straightened out today.

Products of binomials cantake you so long to do a few.

But, just skip the steps anduse FOIL without a big to do.

Figuring out ordered pairscan leave you in such a mess.

But, if you remember thex-axis, y-axis, and origin, you'll do them with success.

Systems of linear equationscan be solved in 4 different ways.

Substitution, additionmethod, determinants, and graphing with different rays.

The slope always equals riseover run.

If you remember this you'llalways get those problems done.

Quotients of 2 polynomialsare called Rational Algebraic Expression.

If you don't reduce themfully they will leave you in a great big depression.

Square roots and cubic rootsleave me very puzzled,

But the index and radicandleave me troubled.

Square-free integers can't bebroken down anymore.

They are like 2,3, and 5, butnever integers like 16 or 4.

There are many other rules,guidelines and steps to Algebra 1

But, we still have Geometry,Algebra 2 and Analysis to continue the fun!!!"

From this poem, I like how theystart off in the same situation as some people who have difficulty withmath. Although really simpleconcepts and the simple differences between rational and irrational, sometimesI still get confused which is which. Next the poem mentions of the basis of algebra, that is in algebra,there are digits and decimals introduced together. Unlike in elementary math, where it is impossible to add anumber with a letter, in algebra, it is possible. In algebra we also learn of exponential problems and usingscientific notations. Forexample, if I want to multiply 10000 by 10000. It would be simpler to express this as 1 x 10^8. Moreover, sometimes learning math thereare tricks or shortcuts. Insteadof doing the regular multiplication problem, I can simply count the numbers ofzeros in both of the numbers and conclude the exponent. So for the above example, there are 8zeros therefore the scientific notation is 1 x 10^8. However, this only applies to some cases where the zeros areending zeros and there shouldn't be any other numbers between the zeros.

One of the significant changes inthe study of math is the understanding of variables. Although variables seem so mysterious at times since we donot know of its value or the number that it stands for, but it is of importantuses especially when calculating an unknown number. Just as in reality, we sometimes have numbers in which weneed to calculate for its unknown, therefore, the use of variables help makesolving problems easier to understand. In the poem, it says, "If you put the right variable in an opensentence, the statement will be true." This means for example, we have an equation like8x-4=20. If you can find a numberfor x, replace it, then calculate it, the number on both sides should be thesame. If it is the same then thestatement is true. Solving thisproblem, the value for x is 3.

Taking the study of mathematics and applying it topoetry, a lawyer from France by the name of Francois Viete had discovered that"the abstract nature of higher algebra depends on its symboliclanguage." (Miller, Charles, page 335) From this quote, I find that "symbolic language"also applies to poetry writing. Sometimes when writing a poem, feelings and thoughts are not expressedexplicitly, but implicitly. Poetstend to use symbols or abstract description to portray what they see, what theyfeel, and what they think. Interms of mathematics, symbolic language signifies the use of letters orso-called variables to represent numbers. This similarity shows that both mathematics and poetry share the samenotation of symbolic usage. Sometimes with symbolic usage, it makes the actual idea of a poem, orthe actual concept of a math problem harder to understand at first if thereader does not have a clue of what the symbol stands for. However, if one is able to make a linkbetween the actual concept and the symbolic representation, understanding comeseasily.

Another point of this poem states that there is apattern in mathematics. Incomparison to poetry, poetry also has a pattern. Pattern makes a poem more stylish and interesting. Patterns in poetry consist of makingeach verse in the poem have the same number of syllables. Or patterns in poetry may consist ofmaking each end word in a verse rhymes with the following verse. Thus, some poems bring about symmetryin its verses. Similarly whenspeaking of mathematics, an obvious pattern that comes to my head is thegeometric series. Especially, whenI consider the Fibonacci sequence, where 1,1,2,3,5,8, … are simply patternsestablished by adding the two previous numbers of the sequence to get thefollowing number. Mathematics also involves symmetry. This is true when one works out a proof, or an equation asthe one above. Taking the aboveequation as an example again, in order to test if x really does equals 3, onewould need to replace x with 3, and so,

8( 3 ) – 4 = 20

24– 4 = 20

20 = 20

Working out this problem, one would see how symmetryis incorporated into math problems. We start off the problem asymmetrically where the right and left sidesof the equation are of different numbers. But to find if the equation is true or not, one needs to work theproblem out and derive both sides to reach the exact same number, thus reachingsymmetry. The above work showsthat the equation is indeed true, since the left side calculates out to become20 and the right side equals to 20 already.

It is believed that in art, people tend to seekpattern, repetition, and mainly symmetry. Taking this belief into account for the discussion of mathematics andpoetry, through our observations and understanding, we do see that mathematicsand poetry are in the form of art also. The other example of symmetry in mathematics is proof. "Mathematician seeks an elegantproof above one which demonstrates the same result through contradiction orexamination of numerous cases."(http://kate.stange.com/mathweb/mathpoet.html) "He seeks the simple, the fundamental from which tobuild his great mathematical structures." (http://kate.stange.com/mathweb/mathpoet.html) From these quotes, I realize howmathematics is not simply developed. But they must be developed with "great mathematicalstructures." As the same withpoetry, if one wants to have a good poem, one must develop a style and followthat style throughout. There aremany ways of writing poetry. Aneasier version of writing poetry is called free writing, where rhymes andcounts do not matter much, but the content itself does. It is up to the human himself as thepoet or the mathematician to design and stylize the structure to make it ascomprehensive and interesting as possible to attract readers or problem solversrespectively. The following quoteis said by Kate Stange to clarify my point. "The artist or poet seeks asimilar symmetry in many ways; the meter of poetry is a subtle counting, andthe words chosen are a concise reflection of the experience of the poet. He seeks to give his poem a contained,elegant form, with verses and stanzas showing the inner symmetry ofthought."

Continuing the discussion of the "AlgebraOne" poem, this poem also refers to the system of linear equations,inequalities, reciprocals, inverses, polynomials, binomials, roots, slopes andordered pairs. From just this onepoem, a quick overview of algebra was introduced. The way the poem was presented was amusing as it has somehumor as well as some friendly comments in it. The tone the poet uses to write this poem centers on an audiencewhom are not so very fond of algebra. Thus I called this poem very friendly to people who dislike mathematics,because through this poem, it may have a positive influence on some of thesetype of people. It may partiallyreduce their hatred in the study of math knowing that there are other people onthe same boat as them.

The poem summarizes that systems of linear equationscan be solved using four different methods. They are substitution, addition method, determinants, andgraphing. Reading this part of thepoem sort of simplifies all those chapters in my textbook and gave me a conciseidea of all the possible methods that can be used to apply to linear equationsystems.

The poem mentions of graphing terms also. It refers to x-axis, y-axis, and originas the key terms that need to be known to successfully create a graph for anequation. In connection to that,there's also the term of the slope introduced, which states how a slope isdetermined. "The slope alwaysequals rise over run." Thisequals the concept of a slope where a slope is the change of y-axis over thechange of x-axis. The"rise" is spoken in terms of the vertical change. And the "run" is spoken interms of the horizontal change.

The poem talks about polynomials and binomials,reciprocals and inverses. Itbriefly gives you a guideline of the importance of these two concepts. I really like this poem because it sortof outlines the poem with the most basic and important concepts that algebracontains. I think it would be avery good introduction to all algebra classes to share this poem. Not only does it has some humor in it,but it also covers a wide range of terminologies and it discusses the mostprominent methods that is used to solve the problems.

Poetry and mathematic are two very distinct topics,yet I find it very similar in its formation and structure. I think the understanding and interestin one may lead into a better understanding and interest in another. I think in general, when we learnsomething, if we are able to grasp some slight idea of just one concept ofsomething which we like, we can very easily build on that concept and expandour knowledge. Similarly, if wegrasp that patterns exist in mathematics, and we enjoy working with patterns,we can easily build our interest in it. I guess, for me, many times I just say to myself, I hate calculating, Ihate working with numbers, I hate solving problems, I hate doing proofs. I never look at a math problem as apoem. But if I had looked at amath problem as a poem, I will see that calculating is essentially the same asfinding a pattern in the poem, working with numbers is the same as counting thesyllables of each verse, solving problems is essentially the same as findingits rhymes at the end of each verse, and doing proofs is essentially the sameas finding symmetry in the poem.

Therefore, in conclusion, although it may soundimpossible to combine poetry and mathematics together at first look, but if onewas to look deeper into the foundation of mathematics and poetry, one will seethat the two have many common perspectives. There was a quote that states: "Mathematics is poetry to one who understands."(http://www.kavaitanjali.com/pgmarch02/onpoetry.htm) And another quote states: "For a person who does not read poetry or knowsmathematics, much of the world is hidden from view." (http://www.kavaitanjali.com/pgmarch02/onpoetry.htm)

Indeed, the knowledge of both poetry and mathematicscombined brought about a realization that no matter how different two thingsmay seem, there still exists some kind of unique link between the two.

References:

Website on the Internet:

1. http: www.teenink.com/past/1990/668.html

2. http: www.ugcs.caltech.edu/~eveander/poem html

3. http://members.aol.com/LooseTooth/poem.html

4. http://teachers. Net/lessons/posts/617.html

5. http//kate.stange.com/mathweb/p_e.html

6. http://www.mathstudio.com/poetry.htm

Information on Books:

Mathematical Ideas by Francois Viete pg 335
The Weight of Number by Baumel Judith
Arithmetic Lesson Infinity: by Linda Pastan
Geometry by Rita Dove
"Pi" by Robert Morgan
The Prince of Algebra by JoAnne Growney