704 WordsDec 11, 20163 Pages

Conclusions: As expected, my hypothesis was correct: If Pascal’s triangle has special mathematical properties (relationship with Binomial Theorem, the sum of the numbers in any row of Pascal’s triangle is a power of two, and the number below two entries across from one another is equal to the sum of both numbers in Pascal’s triangle) , then we can demonstrate, possibly even prove, these properties/relationships through examples, algebraic proofs, and combinatorial proofs because each property concerns binomial expansion, combinations, and combinatorics, thus we can use formulas, counting methods, and simple algebra to prove and illustrate such properties. Pascal’s triangle limits the amount of work necessary in expanding a binomial expression with the Binomial Theorem by eradicating the strenuous process of using the combination formula (n Choose k = n!/k!(n - k)!) to find the binomial coefficients. Effortlessly replace the combinations (n Choose k) with the elements/numbers of the row of Pascal’s triangle, n being the row number, to get the coefficients. Simply put, look at Pascal’s triangle. However, many argue that the construction of Pascal’s triangle for large values of n is a tedious process, but the use of the powers of eleven property contradicts this notion. This property states that: if a row is made into a single number by using each element as a digit of the number (carrying over when an element itself has more than one digit), the number is equal to 11 to the

Related

## Questions On Pascal 's Wager

1833 Words | 8 PagesPascal’s Wager is often considered one of philosophies weakest religious arguments to date. Pascal invents a wager to persuade the one who questions God into attending church, following the Ten Commandments, and following any other traditions in the Catholic Church. The wager is, if a person is a believer and after departing from this earth they find that they are correct, then their rewards are infinite. They will receive eternal life and a relationship with God in heaven. On the other hand if a

## Who Invented the Pascal Triangle? Essay

1896 Words | 8 PagesYou must have heard of the Pascal triangle, how two numbers above add up to the number below and etcetera etcetera, but do you know the person behind the triangle? Who invented the Pascal triangle? Who turned a calculating machine that only existed in dreams into reality? In this report, we will be investigating, not only about what he invented, but he himself as well. He is Blaise Pascal. Our team had decided to research on a Mathematician, because we believe that there is an inspiring yet neglected

## Pascal 's Wager And The Existence Of God

1649 Words | 7 Pagesempirical evidence of a God, wagering for the existence of God will maximize our happiness. Through his wager, one can use simple reasoning to understand that believing in a God which you cannot see may still be the most logical option to live your life. Pascal states that because there is no evidence that a God exists, nor is there any evidence that no God exists, it is entirely possible that a God exists. Wagering for the existence of an almighty God will either bring you eternal life and happiness, or

## The Triangle Of The Bermuda Triangle

1190 Words | 5 PagesEveryone has heard of the scariest place on earth, the bermuda triangle. Since its theoretical existence, there has been hundreds of cases that have been reported that involved the Bermuda Triangle in one way or another. The points of the Bermuda triangle are between Miami, Florida, San Juan, Puerto Rico, and the Mid-Atlantic island, Bermuda. The History of this myth has gone back hundreds of years, dating back all the way to the year 1492, when Christopher Columbus first reported seeing flames

## Questions On Pascal 's Wager

1878 Words | 8 Pagessignificantly stronger of a rationale when more social factors are taken into consideration. In his time, Blaise Pascal formed the foundation of the Pascal’s Wager we know of today, posthumously in the form of ‘Infinirien’. Though this is more easily defensible then Pascal’ Wager, the modified version has garnered enough popularity and has enough similar that it is the target of most criticisms. Pascal came up with a theory of understanding the consequences of not believing in God versus those that came with

## Pascal, The Founder Of The Pascal 's Wager

899 Words | 4 PagesBlaise Pascal was the founder of the Pascal’s Wager. Pascal was a French philosopher, an inventor, a mathematician, a scientist and a theologian. Pascal extended a reason to believe in God, even though other people had beliefs that God is not real and his existence is not inconceivable. The Pascal’s Wager was a second-person communication. It showed that Pascal conceptualizes an individual forced to decide between the belief in God and not to believe in him. An example of what Pascal would demonstrate

## Notes On Blaise Pascal 's Theory Of The Classical Problem Of Modern Economics, Social Science, And Pascal

2312 Words | 10 PagesBlaise Pascal was born on June 19, 1623, in Clermont-Ferrand, France to Etienne and Antoinette Pascal. He was the only son having two sisters, Jacqueline and Gilberte. Blaise Pascal was a person of many hats as he had different traits and talents that he acquired. Not only was he an important mathematician, but also a philosopher, physicist, inventor, scientist, and theological writer. Pascal made numerous contributions to a wide variety of studies that are still appreciated today including a powerful

## Pascal 's Triangle And The Triangle

1086 Words | 5 PagesPascal’s Triangle is named after the seventeenth century mathematician and philosopher, Blaise Pascal. However, several other mathematicians knew about and utilized the triangle before Pascal’s birth in 1623. In the twelfth century, both Persian and Chinese mathematicians were trying to create an arithmetical triangle that is easy to construct and that gives the coefficients of the expansion of the algebraic expression expression (a + b)n for different integer values of n. Pascal’s Triangle was first

## Blaise Pascal Essay

1701 Words | 7 PagesBlaise Pascal Blaise Pascal was born at Clermont, Auvergne, France on June 19, 1628. He was the son of Étienne Pascal, his father, and Antoinette Bégone, his mother who died when Blaise was only four years old. After her death, his only family was his father and his two sisters, Gilberte, and Jacqueline, both of whom played key roles in Pascal's life. When Blaise was seven he moved from Clermont with his father and sisters to Paris. It

## Blaise Pascal Essay

1414 Words | 6 PagesBlaise Pascal "We arrive at truth, not by reason only, but also by the heart"(1) said Blaise Pascal, one of the greatest minds of the 17th Century. The 17th Century was the time of the scientific revolution. During this period the main idea for everyone, was to question everything not to just listen to what is told. This caused a transformation in thought in both religious and scientific areas. Science allowed the questioning of the teachings of the old church. Scientists battled with ideas in

### Questions On Pascal 's Wager

1833 Words | 8 Pages### Who Invented the Pascal Triangle? Essay

1896 Words | 8 Pages### Pascal 's Wager And The Existence Of God

1649 Words | 7 Pages### The Triangle Of The Bermuda Triangle

1190 Words | 5 Pages### Questions On Pascal 's Wager

1878 Words | 8 Pages### Pascal, The Founder Of The Pascal 's Wager

899 Words | 4 Pages### Notes On Blaise Pascal 's Theory Of The Classical Problem Of Modern Economics, Social Science, And Pascal

2312 Words | 10 Pages### Pascal 's Triangle And The Triangle

1086 Words | 5 Pages### Blaise Pascal Essay

1701 Words | 7 Pages### Blaise Pascal Essay

1414 Words | 6 Pages