Blaise Pascal
Blaise Pascal was born on June 19, 1623, in Clermont, Auvergne, France. He was the third child of Étienne Pascal. He was the only male child. Blaise’s mother passed away when he was three years old. After his mother’s death, the family packed their bags up and moved to Paris. Blaise’s father, Étienne decided to teach his son. However, he did not allow Blaise to study mathematics until he was 15 years old. When Blaise was 12, he started to study geometry by himself. Blaise continued his study of geometry throughout his teenage years.

In February 1640, Blaise had his first work, Essay on Conic Sections published. He was only 17 year old at the time. Between 1642 and 1645 Blaise started to develop a digital calculator. He called this device the Pascaline.

In the year 1646, Blaise became very religious and spiritual. He then started working on some experiments dealing with atmospheric pressure. Blaise concluded that a vacuum exists. The famous mathematician Rene Descarte debated Blaise over this issue. Descarte did not believe there was a vacuum. In October 1947 Blaise wrote another book, New Experiments Concerning Vacuums. This caused a lot of debates. After a malignant growth spread from his stomach to his brain, Blaise Pascal died on August 19, 1662 at the age of 39.

Blaise Pascal’s biggest contributions in the field of mathematics deal with probability. He and a French mathematician Fermat sent letters back and forth to each other. They were developing a theory of probability. Pascal also developed a “Pascal’s Triangle.” According to mathematicianspictures.com, “Each number in a Pascal triangle is calculated by adding the two adjacent numbers in the wider adjacent row. The sum of the numbers in any row gives the total arrangement of combinations possible within that group. The numbers at the end of each row give the ‘odds’ of the least likely combinations, within each succeeding pair of triangles giving the chances...

...Pascal’s Triangle is a triangular array of the binomial coefficients. The system after French mathematician BlaisePascal. The set of numbers that form Pascal's triangle were known before Pascal. However, Pascal developed many uses of it and was the first one to organize all the information together in his treatise, Traité du triangle arithmétique (1653). The numbers originally arose from Hindu studies of combinatorics and binomial numbers and the Greeks' study of figurate numbers.
The earliest explicit depictions of a triangle of binomial coefficients occur in the 10th century in commentaries on the Chandas Shastra, an Ancient Indian book on Sanskrit prosody written by Pingala in or before the 2nd century BC.While Pingala's work only survives in fragments, the commentator Halayudha, around 975, used the triangle to explain obscure references to Meru-prastaara, the "Staircase of Mount Meru". It was also realised that the shallow diagonals of the triangle sum to the Fibonacci numbers. In 1068, four columns of the first sixteen rows were given by the mathematician Bhattotpala, who realized the combinatorial significance.
At around the same time, it was discussed in Persia (Iran) by the Persian mathematician, Al-Karaji (953–1029).It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048–1131); thus the triangle is referred to as the Khayyam-Pascal triangle or Khayyam triangle...

...Originally Pascal’s Triangle was developed by the Chinese of long ago. But then the French mathematician BlaisePascal was officially the first person to discover the importance of the patterns it had within itself. But how exactly does it work??? In this research paper, I will explain how to make the Pascal’s Triangle and why it is so special.
Construction:
Pascal’s Triangle is basically a triangle of numbers. “At the tip of the triangle is the number 1, which makes up row zero. Then the second row has two 1’s by adding the 2 numbers above them to the left and right, 1 and 0 (all numbers outside the triangle are zeros). Now do the same for the second row.” 0+1= 1, 1+2=3, 2+1=3, 1+0=1. Then the results become the third row. 0+1=1, 1+3=4, 3+3=6, 3+1=4, and 1+0=1. Then the pattern continues on infinitely.
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There seems to be many patterns in this triangle. For example: The Sums of the Rows.
The Sums of the Rows:
“The sum of the numbers in any row is equal to 2 to the nth power or 2^n when n represents the number of the row.” For example:
20 = 1
21 = 1+1 = 2
22 = 1+2+1 = 4
23 = 1+3+3+1 = 8
24 = 1+4+6+4+1 = 16
Prime Numbers:
“If the 1st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. For example, in row 7 (1 7 21 35 35 21 7 1) 7, 21, and 35 are all divisible by 7.”
The Hockey Stick:
“If a diagonal of numbers of...

...Pascal vs Descartes Paper
Pascal’s argument is fallible because he reaches the conclusion that we should “wager” God’s existence, rather than coming up with “proof” by using deductive reasoning like Descartes provides in his argument. These early 17th century philosophers both provided writings defending the validity of the Christian religion and of God’s existence. After the Protestant Reformation of 1517, the Catholic Church’s sanctity was questioned. Different religions sprouted across Europe and citizens of Western Europe began questioning religion itself and the existence of God. BlaisePascal and Rene Descartes each claimed to have a strong belief in Catholicism (or a denomination of), and because of this strong belief, they sought to defend the validity of the existence of God. Pascal wrote a collection of aphorisms which he started to revise into a writing he would call the “Apology of Christian Religion”. However, Pascal died before he was able to complete it. In Pascal’s Pensees (his writings were collected and organized in the 19th century and 20th century), Pascal systematically dismantles the notion that we, the people, can trust reason to validate God’s Existence. Pascal rambles on about what “we” can’t do to prove God, instead of finding his own proof of God’s existence. His approach to persuade us into believing God is to use mathematical equations and odds to...

...BlaisePascal
“There are two types of minds - the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the dive.” From childhood he was a scientific prodigy. Just from this quote of his you can tell that even his mind in itself can fathom things that none of us even think about on a daily basis.BlaisePascal was born June 19, 1623 in Clermont, France. He was third born out of four children and was Etienne Pascal’s, the father, only son. But at only three years old, Blaise’s mother died, leaving the four children up to Etienne Pascal. In 1632 the Pascal family moved to Paris, France. Blaise’s father had unorthodox educational views and decided to teach his son himself. He said that Blaise was not allowed to study math or science before the age of fifteen. But of course it was impossible to keep his son’s mind away from those two subjects. At just age twelve he started to work on geometry by himself, and before long he realized that the sum of the angles of a triangle are two right angles. When his father found out about this, he gave in and allowed Blaise to have a copy of Euclid.
At age fourteen, Blaise started to attend his father’s meetings. While there he met Girard Desargues and at age...

...The Pascaline
BlaisePascal was born June 19th, 1623 in Clermont. He was the third to be born and the only son. He was kept at home as a child because they wanted to make sure that he was not overworked. His father homeschooled him, but he was not allowed to study mathematics before the age of 15. And because of this there were no mathematical things in the house at all. Soon Blaise gave up his play time at the age of twelve to study geometry.
Between the ages of 18 and 19 the Pascaline was evented by Pascal, Blaise in 1642.It was to help his dad, who was a French tax collector count his taxes. The Pascaline was the first mechanical adding machine. It was 36cm long; 13cm wide; and 8cm wide. It had eight movable parts that added up to eight, figured long sums, and used base 10. Each drum had two sets of rows. The black row of numbers was dealing with addition, and the red row of numbers was dealing with subtraction. The machine was able to convert and exchange rates for different currencies. The pascalines had metal wheel dials that turned to the appropriate numbers, answers appeared in the boxes in the top of the calculator. There were 50 pascalines built, but only few are still present today where you can actually go and see them.
Even though Blaise...

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The Pensees were a marvelous work of BlaisePascal, as he seamlessly attributed so many aspects of his society’s views and beliefs of religion. Firstly, he stressed how pathetic and meaningless the life of a man is, who doesn’t believe in God. His first action is directly faulting the methods of Montaigne. Montaigne, he states, is fickle about his beliefs, switching them by the moment. He further criticizes Montaigne’s beliefs on suicide, death, and salvation. Pascal also believes that man should know himself. By this, he infers that people should attempt to find themselves, and discover their role on Earth. Blaise furthers the criticism on his fellow philosophers by insulting Descartes, and his principle of doubt. Natural intuition, he states, is completely erased by factors in everyday life such as education and other activities. This belief that a life could not be completed without the presence of God made Pascal’s work controversial yet very intriguing.
Pascal saw God in a way that many other philosophic thinkers of his time could not. He believed that God is not simply a mythical being who creates seasons and controls the world’s processes. His belief of God was much higher, as he believed God was responsible for the great human emotions that we possess. These emotions include love, patience, confidence, and benevolence. God, he said, teaches the condition of man, but understands...

... Probability refers to the likelihood or relative frequency for something to happen. BlaisePascal is referred to as the father of probability. Pascal contributed to the branch of mathematics known as probability in 1653. Through his work in probability, Pascal invented the binomial coefficients which are now known as Pascal’s Triangle. Pascal’s major input to the philosophy of mathematics came with his “Of the Geometric Spirit””.1BlaisePascal was also a major contributor to the founding of Statistics.
BlaisePascal contributed to mathematics in many ways, but one of the most important contributions he made was the creation of Binomial Coefficients; now known as Pascal’s Triangle. “Pascal's triangle determines the coefficients which arise in binomial expansions”.1 Pascal’s Triangle has advanced dimension overviews. The three dimensional version is called: “Pascal’s Pyramid”, while the standard one is called Pascal’s simplices. The numbers that are used in Pascal’s Triangle were numbers that were used before; he just integrated them into his invention. A simple explanation of how Pascal’s Triangle is constructed is this: “The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. A...

...Critique on Pascal's Wager
Pascals Wager relies on many assumptions that are not necessarily true, by proving the falsehood of these assumptions the Wager falls apart. First the wager assumes that God cannot tell the difference between true faith and fained faith. Second is that doesn't care if one's willingness to believe is based purely in self interest. Third, if there is a possibility for God to exist there is an equal possibility for him to be nothing like we think. First off what exactly is Pascals Wager.
Pascals Wager goes as follows. If you are incorrect in your belief in God, you lose nothing. That is assuming that death is the absolute end. Also if you correctly believe in God, you gain everything, eternal life and bliss. But if you correctly disbelieve in God, you gain nothing because you end up with death. Whereas if you Incorrectly disbelieve in God, you lose everything and live an eternity of pain. By this logic there doesn't appear to be any reason to not believe in God or at the very least fake it.So to start disproving assumptions we should start with the most glaring one.
Pascals Wager assumes that God, All powerful knowing and good as he is, cannot tell whether your faith is based on true belief or because you are backing into a corner by Pascals logic. Pascal created this wager in order to try and make an argument for faith in God. But the definitive...