Blaise Pascal's Influence On American History

It is said that when history looks upon the life of an individual when their time has passed; it is not the dates on the tombstone that define the man but the dash in between. Such was the case in the life of theologian, philosopher and mathematician, Blaise Pascal. Pascal was born on the 19th of June 1623, in Clermont-Ferrand France and died at the age of 39 of tuberculosis on the 19th August 1662 in Paris, but the bulk of his career, his success and life achievement began in his early years. As a young boy, Pascal’s lost his mother and soon afterward his father moved the family, Blaise and his two sisters to Paris. Pascal’s father, Étienne Pascal was a mathematician himself and taught Pascal Latin and Greek, which at the time was considered

to be a key component of trade and diplomacy. His intent was to introduce Blaise to mathematics when he was older, but Pascal proved to be much more brilliant and talented than his father anticipated. Upon realizing his son intellectual potential; Étienne incorporate mathematics into the boy’s lessons thus enhancing the boys understanding of the mathematical world. Around the age of 12, Pascal’s father began attending discussion groups with other Parisian mathematician and scientist. Blaise began participating in these meetings of the mathematical academy (Académie Parisienne) as well and It was here among the stimulations of thought and reason that Balise Pascal gained skills that would pave the way to his career as one of the greatest mathematician of his time. Pascal’s first achievement was his treaties Essai pour les coniques (Essay on Conics) which he published alongside another book around the age of 16. Even though it was dismissed by René Descartes; the alleged father of analytical geometry and Frances most famous mathematician due to Blaise’s young age. He could not believe that such impressive and complicated works were done by such a young intellect. Descartes skepticism was warranted because Pascal was already introducing concepts such as what later became known as Pascal’s geometrical theorem, the “mystic hexagram, in his Essay on Conics. As explained in [6], Pascal concluded that if you draw any hexagon inside any conic section (the resulting curve of a plane intersects a cone) and then extend the lines of opposite sides, they will meet in three points lying on the same line. His mystic triangle was eventually published and later proved to be the advancement in the world of projective geometry, the study of the properties related to transferring a three-dimensional object to a two-dimensional surface. These accords were only the beginning of Balise Pascal’s influence on the math and science world.
At the age of eighteen, Blaise Pascal constructed an arithmetic machine that was able to add and subtract numbers.

The “Blaise Pascaline,” as referred to in [3] would be considered today as an early version of a calculator. This project derived in part from helping out his father who had been promoted as a tax clerk, a job which required him to perform long calculations at work. Only one other mechanical device was known to add up figures before the Pascaline and that was known as the Schickard's calculating clock, created by German professor Wilhelm Schickard. Unlike Schickard device, Pascal’s calculator had a larger number of production and use despite the somewhat unreliability of the device. The device consisted of a wheel with eight movable parts for dialing and each part corresponding to a particular digit in a number. It worked by using gears and pins to add integers; addends were entered by hand and carriers from one column to the next were broadcast internally by falling weights lifted and dropped by the pins attached to the gears. It could even be manipulated to subtract, multiply and divide if one knew their way around the Pascaline. Subtraction was done by adding the nines complement version of the number being subtracted. Multiplication; accomplished by repeating additions and division performed by repeating subtractions. Balise Pascals went on to inspire directly inspired further work on calculating machines by other inventors such as Gottfried Leibniz and Samuel

Morland.
In 1654, Pascal with the help of Pierre de Fermat developed one of his most significant contributions to the mathematical world, concerning the division of stakes known as the probability theory. In the likely outcomes that an event will occur, Pascal Triangle served as a convenient triangular presentation of binomial coefficient, where each number is the sum of the two numbers directly above it. Pascal provided evidence through defining the numbers by recursion and discovering useful and remarkable patterns among the rows, columns, and diagonals of the numbers. Even though Pascal and Fermat are accredited with a lot of the development it wasn’t the first time that the concept of probability theory was introduced to the known world. It may seem that before the sixteenth and seventeenth century, the realization that one could predict an outcome to a certain degree of accuracy was unheard of but evidence of the triangle has been found as early in the 10th century by Persian mathematician Al-Karaji. It also appeared in the 13th century under the name of Chinese mathematician Yang Hui known then as Yang Hui's Triangle. In the early 1500s Girolamo Cardano (Cardan), doctor and mathematician, wrote a manuscript which presented a somewhat rudimentary definition of probability by addressing the dice scenario in which he pointed out the probability of certain outcomes in rolls of dice and the problem of points. [4] This was the same problem Pascal and Fermat took on as well as the question pertaining to the number of turns required to ensure obtaining a specific number in the roll of two dice.
Pascal’s collaboration with Fermat on the theory of probability was not uncommon. During that time as is common in today, most intellectuals benefited from the assistance of another specialist in their field in order to review concepts and collaborate on resolving questions and scientific inquiries. Like Pascal, Pierre de Fermat was fluent in Greek and Latin and had a passion for geometry. He was considered one of the founding fathers of analytical geometry, finding the perfect balance between algebra with all its formulas and rules and geometry with its use of patterns and shapes and combined them into the highly effective system. He is also known for the development of modern number theory. A theory which examines the profound in the otherwise apparently simple concepts of the way numbers relates to each other.
Among these mathematicians of whom Pascal collaborated include René Descartes. René was even better known than Fermat in the math and his area of study included analytic geometry among other interest. Descartes development of the artesian coordinates allowed the orbits of the planets to be plotted on a graph. His contribution to the century laid down the foundations for calculus and advanced geometry. An original member of the mathematical academy Académie Parisienne, Descartes knew first hand of Pascal’s genius because he had the pleasure of watching him grow and accomplish so much in the geometric world.
Another collaborator of Pascal’s work was Gottfried Wilhelm von Leibniz. Unlike the for mentioned mathematician who knew Pascal personally, Leibniz collaboration with Pascal was more of a continuation of his work. In 1671 with the goal of improving upon Pascal’s calculating device the Pascaline, Leibniz began working on a prototype calculating machine that was going to improve the Pascline by making it is able to multiply and divide. On February 1, 1673, Leibniz demonstrated a wooden model of his calculator at the Royal Society of London. Although his model did not yet reach the standard that he wanted, Leibniz’s vision of an easy fast and reliable calculation tool with an adjusted size so the numbers being calculated as large as desired [9], came true and these features can be observed in any modern calculator today.
The 17th century was an exciting time in the world for math and science. The past hundred years had been filled with new exploration of space and time which cultivated a curiosity that propelled man into the new era with a hunger for logic and reason. At the beginning of the century John Napier, a Scottish landowner and mathematician, invented the logarithm. The logarithm, which was improved by Henry Briggs alongside Napier, contributed to the advance of science, and mathematics by making some difficult calculations relatively easy using the mathematical operation to determine how many times a certain number (the base) is multiplied by itself to reach another number. Using Napier’s logarithms other 17th Century mathematicians like Johannes Kepler and Isaac Newton were able to develop their innovations through accurate and complex calculations. It seems that the seventieth century was the father of mathematical geniuses, with many a great mathematicians, alongside Pascal, being born in that era. Isaac Newton was and still is one of the most renowned mathematicians to ever live. Born January 4, 1643, two decades after Pascal, Newton excellence in physics and math contributed immensely to the scientific world. In terms of mathematics, he contributed to the study of power series, generalized the binomial theorem to non-integer exponents, developed Newton’s method for approximating the roots of a function, and classified most of the cubic plane curves not to mention his title as one of the developers of calculus. [10] Newton was also the father of the Mathematical Principles of Natural Philosophy and for coming up with a mathematical description of gravity.
Another mathematician of great esteem born in the 17th century was Christopher Wren; born October 20, 1632, in East Knoyle, England. Like Pascal as a child, Wren showed capacity for science, drawing and building mechanical objects.[11] As he got older his achievements were numerous. In terms of his success as a mathematician, Christopher Wren was known for his modification of the cycloid. Most of the properties of the curve had been discovered by none other than Pascal himself, but Wren was the one to adjust it so that he found straight a line equal to an arc of that curve. He is also most famously known for designing and rebuilding new churches after they burned down in a great fire in London.