Blaise Pascal Kevin Kappenman Blaise Pascal's life Blaise Pascal was born on June nineteenth in the year 1623. He was born in a town called Clermont-Ferrand, in France. His father, Etienne Pascal was a judge at the tax court in Clermont-Ferrand, and his mother died a few years after Blaise Pascal's birth. Blaise was the third of four children that the family had and was the only son. After his mother's death Etienne Pascal moved the family to Paris, France where Blaise was educated at home. The studies that Pascal pursued specifically omitted the study of math. Etienne believed that the study of mathematics would prove so fascinating that Pascal would be unable to focus on any of his other classical studies, and so Pascal was forbidden from learning mathematics. Pascal pursued the study of literature and the humanities as instructed by his tutors, but of course the elusive subject sparked Blaise's attention and he began to study geometry, and discover geometrical concepts on his own. It has been said that Pascal began drawing geometric figures during his free time. He drew these figures with such accuracy that he was able to begin to study them. It is said that Pascal was able to determine that the sum of all the angles in a triangle added up to two right angles all on his own. He did this by folding the triangle in such a way that the edges lined up and the sum was clear. When Etienne saw how well the boy had taken to mathematics he gave Pascal a copy of Euclid's Elements to study and allowed Pascal to attend meetings of the mathematical society of which his father was part, Academie libre. It was through these meetings that Pascal came into contact with the latest findings in mathematics. His study of mathematics continued to grow and would culminate to new heights throughout his life. In 1640 the family moved to Rouen where Etienne had received a new position as a tax collector. It was here in Rouen that Blaise began a spiritual revolution. When Pascal's father injured his leg he was cared for by a pair of Jansenist converts. In the process of caring for Etienne their religion impacted Blaise who proceeded to become devoutly religious. The Janesites offered a religion different from the Jesuit practices that were common in the area. The Janesites lived with the Pascal family for almost a year while Etienne recovered from his broken leg. In the year 1654 Pascal went through an experience that he believed to be a call from the Heavens to abandon the trivialities of the world. While he was riding a horse drawn carriage the horses ran wild toward the edge of a bridge, he was only saved when the train, connecting the horses to the carriage, broke. He moved to Port Royal and began to study and contemplate religion. It was his religious and philosophical works for which he is said to be best known. The first such work is Les Provinciales which were a blow against the lax morality of the Jesuits. These works would be read by many different religious sects. A future Pope, Innocent XI corrected many of the points that Pascal had brought up within this work to help return to the Catholic religion to a more focused position. Pascal also began working on the Apologie, but this work remained unfinished upon his death. The work was published under the title Pensees. This work was compilation of fragments and notes that Pascal had written that told of the failures of mankind, as well as the infinite glory and importance of Christ. Although Blaise Pascal is often thought of in terms of Physics and Mathematics, it is his works in religion that are often overlooked. Blaise Pascal died in 1662. He was only thirty nine years old at the time of his death. The cause of death for Blaise Pascal is a bit of a mystery. It was assumed to be tuberculosis until an autopsy was performed after his death. The autopsy revealed problems with his stomach and a lesion in his brain. The problems with his stomach seem to be stomach cancer, although that was not a diagnosis given in 1662, and the lesion in his brain could be responsible for his chronic headaches. The cause of death generally accepted is tuberculosis, but with these other physical organ problems more issues may have caused his death. Blaise Pascal's works in Science and Mathematics Pascal's fascination with mathematics began due to the fact that his father forbid the subject from being taught at a young age. He discovered some of the basics in geometry on his own, such as the sum of the interior angles of a triangle. He began seriously working with mathematics soon after his father introduced him to the group, Academie libre. In front of the group of mathematicians Pascal began to present some of his early mathematical works. One of his early theorems involved his mystical hexagon the idea behind his hexagon is that if a hexagon is inscribed within a circle then the three intersection points of opposite sides all lie on a single line. He named this line the Pascal line. Around this same time Pascal began developing his work with conic sections. Pascal's work on conic sections was written in the essay Essai pour les Coniques, essay on conics. In this essay his work with the mystical hexagon could be found. The work also contained hundreds of propositions on conics. One of these ideas involved a quadrilateral inscribed in a conic, and a straight line cutting the sides taken in order in the points A,B,C,D , and then the conic P and Q, this means that P A:P C : P B:P D = QA:QC : QB:QD This formed an interesting new way of looking at the relation between a quadrilateral and a curved conic section. The source of his information for this work came from studying Apollonius and his successors. By building upon the developments of the past Pascal developed his own new ideas. This work containing his ideas served as a big step in projective geometry, taking a three dimensional figure and placing it on a two dimensional plane. This work was published in 1640, when Pascal was only seventeen years old. It was around this same time that Pascal began to study Torricellis experiment. This experiment involved overturning a tube of mercury into a bowl that was also filled with mercury. The mercury would fall to a certain point in the tube and then stop. This was used as a way to estimate the weight of the atmosphere. The vacuum created by the falling mercury would pull the mercury up the tube to varying heights based upon the atmospheric pressure. Pascal continued this experiment with many variations. He performed this experiment on a mountain overlooking his birthplace of Clermont-Ferrand, as well as in Paris to determine that the level of Mercury in the tube changes along with changes in elevation. This led to Traite du vide (Treatise on a Vacuum) being published. 2 The equation developed from Torricelli's experiment is as follows: Pressure = (Density of Mercury) · (Height of Mercury) · (Earth's gravitational constant) This allowed for atmospheric pressure to be calculated, Earth's gravitational constant has been found to be 9.8. From his work in physics with the atmospheric pressure on the bowl of Mercury Pascal also came to develop the syringe and a hydraulic press which used a principle now known as Pascal's Law. This law states that pressure applied to a confined liquid is transmitted through the liquid regardless of the area of the applied force. (Force on one side)=(Area of applied force) = (Force on other side)=(Area of applied force) In essence this means that any force applied to a liquid in a confined space can be transferred through the liquid to a new direction. These works were an impressive step in physics. When Pascal's father became a tax collector in Rouen he began working on a very interesting machine. It was an early form of the calculator, capable of simple addition, subtraction, multiplication, and division. He called the machine a Pascaline. The Pascaline had eight movable dials that represented numerical digits such as ones, tens and hundreds. Pascal attempted to sell models of his Pascaline, but it was not well received and quickly went out of production. In 1650 Pascal began work with what he hoped would be a perpetual motion machine. The idea behind the machine was that it would produce more energy than was consumed in setting the machine in motion. Such a device would have solved the world's energy problems before they started. The attempts to build such a device failed. However this did lead to Pascal's wheel, which he named the roulette machine. Roulette being the French word for little wheel. The Roulette gambling wheel was developed in the eighteenth century and was loosely based upon Pascal's version. In 1654 Pascal began his work with his famous triangle. It is an easy tabular method for finding the binary coefficients of a multiple of binary terms. Each number in each subsequent line, down the triangle, is the sum of the two numbers to its right and left in the row above it. A binomial is an algebraic expression that is fairly straight forward, it involves two numbers, call them a and b, these numbers are then raised to a power as follows.