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 17th 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.
Later, an itinerant teacher, Zhu
Shijie traveled across China in the later part of the 13th 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” (16th
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” (16th
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” (17th 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
“16th
Century Mathematics – Tartaglia, Cardano, and Ferrari” The Story of Mathematics. https://www.storyofmathematics.com/16th_tartaglia.html
“17th
Century Mathematics – Pascal.” The Story
of Mathematics. https://www.storyofmathematics.com/17th_pascal.html
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Pascal's triangle made its first appearance in Europe in Jordanus de Nemore's Arithmetic (13th century). Gersonides used the multiplicative formula to determine the binomial coefficients in the early 14th century. The whole triangle was published on the frontispiece of Petrus Apianus' (1495–1552) book on commercial calculations in 1527. In 1544, Michael Stifel published a section of the triangle (from the second to the center column in each row) as a table of figurate numbers. Tartaglia's triangle is the name given to Pascal's triangle in Italy, after the Italian algebraist Niccol Fontana Tartaglia (1500–1577), who published six rows of the triangle in 1556.
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