Blaise Pascal was born at Clermont on June 19, 1623 as the third of four children and the only son to Étienne Pascal. Blaise grew up without a mother, who died when he was only three years old. His father had dissident educational views and decided to educate his son himself, however, Étienne decided that Blaise was not to study mathematics before the age of fifteen. Therefore, he removed all mathematic texts from their house.

Although he was told not to study mathematics, Blaise became curious and began to work on geometry himself at the age of twelve. He discovered that the sum of the angles of a triangle is equal to two right angles. When his father found out, he gave in and allowed Blaise to have a copy of Euclid's Elements, a book written by a Greek mathematician best known for his treatise on geometry. From there, Blaise expanded his knowledge of mathematics and soon began to accompany his father to Mersnne's meetings. Mersenne was known for his work in number theory and was idolized by many scientists and mathematicians. At the age of sixteen, Pascal presented a piece of paper at one of the meetings, which conained a number of projective geometry theorems, including Pascal's mystic hexagon. Many people were amazed.

Blaise showed a very keen interest in mathematics, and went on to publish a highly appreciated treatise called "Essay on Conic Sections." Conic sections deal parabolas, hyperbolas, and an ellipse which can be obtained by intersecting a plane with a double sided cone. Only two copies are known to have been printed, and at the time, his essay attracted little attention. Many people questioned how a sixteen year old could write something that seemed so mature for his age, and believed he had simply read and copied it from someone else. However, Gottfried Leibniz, a German philosopher and mathematician, realized that Pascal had made a remarkable advancement in the study of conics and Girard Desargues, founder of geometry, spoke highly of his...

...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...

...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...

...BlaisePascalBlaisePascal 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...

...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...

...
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...

...Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle.It is also known as the figurate triangle, the combinatorial triangle, and the binomial triangle. Even though Pascal’s Triangle is named after seventeenth century mathematician, BlaisePascal, several other mathematicians knew about and applied their knowledge of the triangle hundreds of years before the birth of Pascal in 1623. The Arabs, Persians and the Chinese discovered Pascal’s triangle in earlier centuries.
The earliest depictions of a triangle of binomial coefficients occur in the tenth century in commentaries on the Chandas Shastra. The Chandas Shastra was an ancient Indian book on Sanskrit prosody written by Pingala between the fifth and second centuries BC. Though Pingala's work was found in fragments, 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 were sums to the Fibonacci numbers. The Indian mathematician Bhattotpala later gave rows 0-16 of the triangle.
Around the same time, the traingle was discussed by mathematicians in Persia, Al-Karaji,and mathematician Omar Khayyám, reffered to the traingle as the "Khayyam triangle" in Iran. Many theorems related to the triangle were known, including the binomial theorem. In fact Khayyam used a method of finding nth roots based on the binomial...

...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...