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So yes, this is me talking about math. Shocker, since I soooo love math. Did you hear the sarcasm? To finish my degree, I had to take one more math class. That was almost a deal breaker for me until I found out I could take a history of math course that would suffice. So this is a history paper on mathematics. Go me!

The
concept of Pascal’s Triangle has been around for centuries, although it wasn’t
given that name until the 17^{th} century. The Persians and the Chinese
both appear to have discovered the application independent of the other in the
eleventh century. In Persia, Omar Khayyam was extracting number roots with the
triangle. Khayyam was a teacher of geometry and algebra, and studied astronomy
and the Jalali calendar. He was also an “advisor to Malik Shah I” (Famous
Mathematicians 1) until Shah was murdered. In 1070, Khayyam’s finished writing
his treatise called *Treatise on
Demonstration of Problems of Algebra*. Within it “he laid the foundation of
the Pascal’s triangle with his work on triangular array of binomial
coefficients” (Famous Mathematicians, 1). This treatise was not only highly
influential in Persia, but made its way across Europe as well.

*The Yellow Emperor’s detailed solutions to the Nine Chapters on the
Mathematical Art or Huangdi Jiuzhang Suanjing Xicao*, and a collection of
mathematical rules called *Suanfa Xuegu Ji*.
After Jia Xian’s discovery, Chinese mathematicians continued to look at the
triangle’s binomial coefficients, trying to take it further. A few centuries
after Jia Xian, in 1261, one of these mathematicians, Yang Hui, (writer name of
Qianguang) wrote an analysis of the mathematical rules in *Huangdi Jiuzhang Suaniing Xicao *in great detail (Beard, 1). Because
of Hui, the work of Jia Xian has survived even though his book perished. In his
preface, Hui explains his intention to make Jia Xian’s work better known,
including his understanding of the triangle with his table “which records the
coefficients up to the row 1 6 15 20 15 6 1” (Mac Tudor, 1). Very little is
known about the life of Yang Hui, except for the works he left behind in reclassifying
the ancient mathematical works of those mathematicians who came before him.
Because of his efforts in preserving the ancient methods, in China the triangle
is often referred to as the Yanghui triangle.

Later, an itinerant teacher, Zhu
Shijie traveled across China in the later part of the 13^{th} century. He
was considered one of the greatest mathematicians of China. He is best “known
for having unified the southern and northern Chinese mathematical traditions”
(Horiuchi, 1). In 1303 he published *Siyuan
yujian* or “Precious Mirror of Four Elements” which showed a diagram of the
triangle, which was labeled the “Old Method”, proving that the concept was much
older.

Zhu Shijie's
illustration of Jia Xian's triangle. Image courtesy of Encyclopeadia
Britannica, Beard

In Italy, another mathematician Niccolò Fontana, came onto the mathematics
scene. In 1535, Bologna University held one of their public mathematics
competitions where Fontana revealed a solution that had been considered
impossible. He later “devised a method
to obtain binomial coefficients called Tartaglia’s Triangle” (16^{th}
Century, 1). Due to an injury, Fontana stammered and was called Tartaglia,
which means “the stammerer”. Even though
he produced many formulas, he “died penniless and unknown” (16^{th}
Century, 1). Which brings us to Blaise Pascal.

Much later in 1654, French
philosopher and mathematician Blaise Pascal wrote a treatise on the triangle
named *Traité
du triangle arithmétique* (*Treatise on Arithmetical Triangle*). It was
published in 1655.

Blaise
Pascal was both religious and a scientist. “He laid the foundation for the
modern theory of probabilities, formulated what came to be known as Pascal’s
principle of pressure, and propagated a religious doctrine that taught the
experience of God through the heart rather than through reason” (Jerphagnon,
1). Syringes, hydraulic pressure, the barometer, and the first type of
calculator, among many other contributions of science, can all be linked back
to Pascal, including the triangle named after him. Although Pascal didn’t
discover the triangle first, he “made the conceptual leap to use the triangle
to help solve problems in probability theory” (17^{th} Century, 1).

__References__

Beard,
Andrea. Yang Hui: Chinese Mathematician. *Encyclopaedia
Britannica*. https://www.britannica.com/biography/Yang-Hui

*Famous Mathematicians*.
https://famous-mathematicians.com/omar-khayyam/

Horiuchi,
Annick. “Zhu Shijie: Chinese Mathematician.” *Encyclopaedia Britannica.* https://www.britannica.com/biography/Zhu-Shijie

Hosch,
William H. *Encyclopedia Britannica* https://www.britannica.com/science/Pascals-triangle.

“Jia
Xian” *Mac Tudor*. http://www-history.mcs.st-and.ac.uk/Biographies/Jia_Xian.html

Jerphagnon,
Lucien, et al. “Blaise Pascal: French Philosopher and Scientist.” Encyclopaedia
Britannica. https://www.britannica.com/biography/Blaise-Pascal

Kazimir,
Jessica. “Pascal’s Triangle.” *Montclair
University*. http://pages.csam.montclair.edu/~kazimir/history.html

“16^{th}
Century Mathematics – Tartaglia, Cardano, and Ferrari” *The Story of Mathematics*. https://www.storyofmathematics.com/16th_tartaglia.html

“17^{th}
Century Mathematics – Pascal.” *The Story
of Mathematics.* https://www.storyofmathematics.com/17th_pascal.html

I really related to the
matter-of-fact tone of “The Things They Carried” by Tim O’Brien. There have
been times when the only way to get through talking about something had to be
very clipped and matter-of-fact in order to keep my vocal chords from closing off.
I had a terminally ill child and so many times I’d be in the emergency room
rattling off previous medications and surgeries and what brought us there this
time with the seemingly emotion of a stone all the while my heart was racing
and I held back my fear because once I let it loose, I’d be weeping
uncontrollably. The stark tone as the supplies they carry are listed with
things interspersed such as “They carried the sky. The whole atmosphere, they
carried it, the humidity, the monsoons, the stink of fungus and decay, all of
it, they carried gravity” (O’Brien 1184) felt so familiar as when I rattled off
the weight of my son’s mortality that I was trying futilely to bear. It also
weaved in the setting of the jungles of Viet Nam in a way that made the life of
the soldier so bleak and enduring to the point that the horribleness of it
became mundane, which makes it all the more awful seeming as a reader.

Yet in the end Lieutenant
Cross strips the weight of the world and home and love from his rucksack
because to be a true soldier, a responsible leader of soldiers. He had to let that all go in order to bear the
heavier artillery of the burden soldiers bear. Everything else is gone,
stripped away. “Commencing immediately, he’d tell them, they would no longer abandon
equipment along the route of march. They would police up their acts” (O’Brien
1189) “He would not tolerate laxity. He would show strength, distancing
himself” (O’Brien 1190).

In comparison, the
hateful, dark tone of The Cask of Amontillado came out gleeful in a macabre
sense that matched the setting of the underground chilly vaults where wine was
kept amid the family tomes and stacked bones of the dead. My takeaway of the
theme? Never trust someone you have wronged, especially if they are offering
gifts and are overly cheerful. When Fortunado is told “we will go back; your
health is precious. You are rich, respected, admired beloved: you are happy, as
once I was. You are a man to be missed” (Poe, 1128) he should have run for the
hills instead of going further into the depths of the vault. I’m kind of
shaking my head at this one as Fortunado should have known better. I feel about
as sorry for him as the woman in a horror show who goes down into the basement
when she hears a noise.

Work Cited

O’Brien, Tim, “The Things They Carried.” Abcarian, Richard,
Marvin Klotz, and Samuel Cohen, eds. *Literature: The Human Experience:
Reading and Writing*. New York: Bedford/St. Martin’s, 2016, pp. 1177-1190

Poe,
Edgar Allen, “The Cask of Amontillado.” Abcarian, Richard, Marvin Klotz, and
Samuel Cohen, eds. *Literature: The Human Experience: Reading and
Writing*. New York: Bedford/St. Martin’s, 2016, pp. 1126-1131

image;

"The Things They Carried by Tim O'Brien" by manhhai is licensed under CC BY 2.0

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