# Pascal's Triangle Essay

Great Essays
Introduction I’m going to start this paper with introducing the history of Pascal’s Triangle, time ranging from 2nd century BC to 18th century AD. Among all the academic works by ancient mathematicians, I’m going to focus on Jiu Zhang Suan Shu [Nine Chapters on the Mathematical Art] composed by Chinese scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After that, I will introduce Jade Mirror of the Four Unknowns written by Zhu Shijie around 14th century AD. My focus will be his idea of using the “four unknowns” to convert a problem into a mathematical system of polynomial equations. Later on, I will also …show more content…
A literature of Pascal’s Triangle emerged in 1068 discovered by Hindu mathematician Bhattotpala (c.1068) who recorded the first 16 rows of the triangle (Wilson, 2013, p170). Meanwhile, in Persia, Al-Karaji (953-1029) also found the binomial theorem according to Pascal’s Triangle as well as several theorems related to it (Coolidge, 1949, p151). Although the original work from Al-Karaji had lost, the later Persian mathematician Khayyam (1048-1122) referred Al-Karaji’s work about Pascal’s Triangle and uses it to find the nth roots according to the binomial expansion. Also around 11th century, Chinese mathematician Jia Xian (1010-1070) used Pascal’s Triangle to extract square roots and cube roots – more details will be mentioned later in this paper. He wrote down his discovery in the book Shi Shuo Suan Shu [The key to Mathematics]. Although the original book has lost, the later mathematician Yang Hui (1238-1298) mentioned in his book that he was inspired by Jia’s work and found out more theorems and applications related to Pascal’s Triangle (Qian, 1981, p56). Moreover, the earliest display of Pascal’s Triangle was also from Yang Hui’s work. The following is how Yang Hui display the …show more content…
The book was composed around 2nd century BC to 10th century AD with no exact date could be tracked. But what we can know is, The Nine Chapters on the Mathematical Art is the basis of ancient Chinese mathematics, which is designated as the math textbook in Tang and Song dynasty (7th – 13th century BC) and widely spread in Asian countries. That period of time is also called the golden age of Chinese mathematics (Straffin, 1993,

## Related Documents

• Improved Essays

Nikhita Guntu and Laya Biddala Archimedes Background Information: Archimedes, (born c. 287 bce, Syracuse, Sicily,—died 212/211 bce, Syracuse), the most-famous mathematician and inventor in ancient Greece. Archimedes was the son of the mathematician and astronomer named Phidias. There is very little information left behind on Archimedes’ family.…

• 730 Words
• 3 Pages
Improved Essays
• Decent Essays

There are many famous and influential mathematicians that have done many wondrous and extraordinary things, some of these range it Einstein, newton and to pascal. But one interesting one in particular is Pythagoras. Pythagoras is one of the many famous mathematicians that has lived on the earth. What he did in math helped shape math to what it is today. Some things he did was learn math and science as much as he could, create the useful Pythagoreanism, and help progress the advancement of mathematics.…

• 476 Words
• 2 Pages
Decent Essays
• Improved Essays

Dorothea Rockburne’s deep interest of mathematics influenced her artwork (30). Dorothea Rockburne’s work, Pascal’s Provincial Letters, was focused on the inherent relationship between the rectilinear shapes of multiple colors shown against a backdrop of deep, dark undertones of blue. Contemporary artists, like Rockburne, take in consideration of current ideas and force the audience to rethink the familiar. In this piece, Dorothea Rockburne uses a contemporary color scheme, lines, and shapes in Pascal’s Provincial Letters, in order to demonstrate the theme of contemporary art which mirrors contemporary culture and society. Dorothea Rockburne uses multiple different colors throughout her painting.…

• 434 Words
• 2 Pages
Improved Essays
• Improved Essays

Many historians believe that the start of many Western societies began with the Greeks. They Greeks have made many contributions to make their lives easier and these advances have also helped shape Western civilizations. The Greeks have spent their lives making contributions in many areas such as math, philosophy, and government. Many of the concepts in math that students learn in school is based on contributions made by Greek mathematicians.…

• 617 Words
• 3 Pages
Improved Essays
• Improved Essays

In his book, The Joy of Pi, David Blatner, the author of fifteen books on various subjects, attempts to explain why mathematicians continue to approximate pi to this day. He believes that they continue to do so because it poses a challenge, and it is in human nature to conquer that challenge. He tries to relay this belief to his readers through a number of different methods including, a history of pi, explaining why pi is fascinating, and how pi appears in the natural world. His writing style, text format, book format, and content all excellently cater towards the non-mathematically oriented, but still educated audience. David Blatner’s book, The Joy of Pi, attempts to show the reader, who may not necessarily be a mathematician, why mathematicians…

• 1273 Words
• 6 Pages
Improved Essays
• Improved Essays

“ Neither the Han nor the Roman empire emerged through a sudden, unexpected revolution”. The Han empire was controlled by Shi Huangdi was a chinese monarch who was awed by his advisors by the scale of his success. while there was also the great empire of Rome that was controlled by Octavian who later went under the new name Augustus who like Shi Huangdi became a monarch both had multiple achievements while rule their empires and both used this titles and justified their actions because of their political power showing “How the builders of the Han and Roman empires conceived and justified their political authority Starting with the Han empire source 1 of the packet titled “ From Sima Qian” which is a biography that describes Qin Shi Huangdi…

• 1116 Words
• 5 Pages
Improved Essays
• Improved Essays

Chinenyenwa Amaechi Dahiya AP Calculus 16 October 2015 Every student who has ever asked an older adult for help with their math homework is very familiar with the phrase “This is not the type of math I did growing up”. The mathematics we have today greatly differs from that of earlier generations and time periods due to the dynamic nature of this field of study. Throughout history, many important individuals have contributed to the field of mathematics and have helped develop the theories, postulates and mathematical rules which are widely accepted today. From the quadratic formula to the trigonometric functions, these people have revolutionized the way we view mathematics in unimaginable ways.…

• 1094 Words
• 5 Pages
Improved Essays
• Superior Essays

In this paper I will explain and critique an argument known as Pascal’s Wager. I will explain the wager Blaise Pascal proposed to incline atheist and agnostics to believe in God. The Wager, “is not a proof of Gods existence” (Furman). I will give Pascal’s reasoning for explaining why choosing to believe in God is the best decision one could make. Pascal’s Wager is an argument given to atheist and agnostics to show them why believing in God’s existence is the right choice.…

• 1632 Words
• 7 Pages
Superior Essays
• Improved Essays

Women’s role of ancient China was once significant. They could rise to power holding high positions, controlling armies and even possibly becoming empresses. However, as time changed so did the view of the women’s role. Men began to take control and began teaching a new attitude towards women such as the admonishment from the ‘Book of Odes” (Shijing) writing: Clever men build cities; Clever women topple them…

• 805 Words
• 4 Pages
Improved Essays
• Improved Essays

The Ontological Argument and Pascal’s Wager The “Ontological Argument” was created by Saint Anselm; this argument is in support of God’s existence. His argument is one based on observation and reason not on empirical evidence and is spit in to three parts. The parts include why god exists, why god cannot be thought to not exist, and lastly why atheists are able to think that God does not exist. In the first section he begins with a definition of God that he believes everyone would be accepting of and that cannot be disputed.…

• 1583 Words
• 7 Pages
Improved Essays
• Improved Essays

Blaise Pascal’s basic belief was that all people have to just take a 50/50 wager for the existence of God. His claim comes from his belief that there is no reasonable way to support either side of the argument about the existence of God. Although Blaise Pascal was a brilliant French philosopher, mathematician and physicist, his claim that there is no creditable evidence to support a reasonable belief about God is not completely correct. It is just an easy way to completely avoid an intelligent quest of the existence of God. We can see clear proof for both the true existence of God and thus proof that Blaise Pascal was incorrect.…

• 1109 Words
• 5 Pages
Improved Essays
• Improved Essays

The Doctors' Plague: Germs, Childbed Fever, and the Strange Story of Ignác Semmelweis (Great Discoveries.) By Sherwin B. Nuland. 191 pp., illustrated. New York, Norton, 2003. \$21.95.…

• 959 Words
• 4 Pages
Improved Essays
• Improved Essays

Arthur Cayley had a pretty amazing life. He was born on August 16, 1821 in the United Kingdom. His mom was Maria Antonia Doughty and his dad was Henry Cayley, he also had one brother Charles Bagot Cayley. Cayley always had a love for math, even at a young age. He was sent to a private school in the United Kingdom up until he was fourteen years old.…

• 512 Words
• 3 Pages
Improved Essays
• Improved Essays

Science, Math, and Technology in Ancient China In the modern world, especially in The U.S., we often think that we are more advanced than other cultures through the ages. And while we may be more technologically advanced in terms of electronics and such, could we have built the pyramids, could we have built the colosseum, or could we have built Alexandria’s Lighthouse using the current technology of the day. I don’t think we could and this paper goes on to impress on you the humbling view that we are not smarter than people in the ancient world, but that we have more accumulated knowledge.…

• 1191 Words
• 5 Pages
Improved Essays
• Improved Essays

Archemetes the War Hero William Catanese Archimedes is considered one of the most known mathematicians, physicists, engineers, and inventors of ancient times. Although much of his life is unknown, he is still a great contributor to mathematics, in which he did modern calculus and associated mathematics to physical occurrences, Founding Hydro statistics, which include an exclamation of the principle of the liver. Archimedes has also originated an exact number for pie, explaining the spiral it's name is known for,and making a system we use today of exponents. He is know for making groundbreaking inventions such as the screw, and making a system we use today of exponents. He is also know for making inventions like the screw, The Claw of Archimedes, the Archimedes Death Ray, and other war machines to protect Syracuse from invasion.…

• 582 Words
• 3 Pages
Improved Essays