Pascal ● A brief introduction to Pascal by mathematician Pascal?

"Pascal showed precocious mathematical genius, but his activities in this field were hindered by religious scruples ... Nevertheless, he made remarkable progress in several different branches of mathematics and physics." -Wolff

"Mathematics is the highest exercise for the spirit." pascal

Pascal is a French mathematician, physicist, philosopher and essayist. He was born in clermont-ferrand on June 1623. 1662 died in Paris on August 19.

Pascal lost his mother at the age of 4, and his father was a well-read and versatile government official. He is an amateur mathematician. Because Pascal was weak and sickly since childhood, his father kept him from getting into math too early, lest he think too much. When Pascal 12 years old, he saw his father reading geometry and asked what geometry was. In order not to let him know too much, his father simply told him that geometry is to learn graphics, and soon put away his math book. His father's "ban" on his contact with mathematics aroused Pascal's curiosity about mathematics. So Pascal did his own research. When he told his father that the sum of the three internal angles of an arbitrary triangle is 180 degrees, his father shed tears of excitement and changed his original idea. Pascal was asked to learn classical mathematical masterpieces such as "The Original" early, and Pascal greedily finished reading "The Original" quickly.

Pascal is a legend in the history of science. He was once described as the greatest "anecdote" in the history of mathematics. /kloc-D'Alembert, a great mathematician in the 8th century, praised his achievement as "the intermediate link between Archimedes and Newton".

Pascal showed amazing precocity: at the age of 1 1, when he tapped the food plate with a knife, it made a sound, and when he pressed the plate with his hand, the sound stopped abruptly, which inspired him to write a paper on the pronunciation of vibrators. At the age of 12, he independently discovered many theorems in elementary geometry, including that the sum of the internal angles of a triangle is equal to 180? ; /kloc-the coefficient of binomial expansion found at the age of 0/3-"Pascal triangle"; /kloc-at the age of 0/4, he was allowed to attend the weekly scientific seminar hosted by Mei Sen (from which the French Academy of Sciences developed). 1653, he wrote arithmetic of triangular array, which was revised and published in 1665. In this book, the basic principles of probability theory and some theorems about combinatorial theory are established. Together with Fermat, he laid the foundation of probability theory and combinatorial theory, and gave a series of answers to questions about probability theory. When Leibniz later read Pascal's research results in this field, he deeply realized the importance of this "new logic". In addition, Pascal's "triangle array arithmetic" includes the earliest mathematical induction.

When Pascal was less than 16 years old, he was inspired by the works of the geometer Dasaga, and discovered the following famous theorem: "If a hexagon is inscribed with a conic, the intersection of its three pairs of opposite sides is a line, and the inverse proposition is also established." So, he wrote a paper on conic curve, which was published in 1640.

Italian mathematician cavalieri once suggested that the area of a triangle can be calculated by dividing it into countless parallel straight lines. In order to get rid of the logical defects in cavalieri's method, Pascal thinks that a line is not composed of points, but of countless short lines. A face is not composed of lines, but of countless facets; A solid is not composed of a surface, but of countless thin solids. Following this clue, he calculated the area (equivalence) of the trapezoid with curved edges under the curve, and calculated the area of the cycloid and the volume of its rotating body. Pascal's study of geometry with infinitesimal reached a high level at that time, but because the concept of infinitesimal is not clear, its indispensability is also mysterious. When others ask questions, he answers their criticisms with "I got the message". Pascal believes that nature provides infinity and infinitesimal to people not for understanding, but for appreciation. He saw that infinity and infinitesimal are mutually restricted (in a reciprocal relationship). He denies that graphics are composed of low-dimensional elements, and thinks that the difference between discrete and continuous disappears with the application of analytical methods. His thought is the strict definition of future limit and infinitesimal and the establishment of calculus. He made an in-depth study of cycloid, and wrote the masterpiece On Cycloid in 1658, which solved many problems about cycloid. This book has a profound influence on young Leibniz.

Pascal designed the world's first mechanical computer at the age of 18.

In physics, 1648, he proved that the air has pressure through experiments, which shocked the whole scientific community, thus completely smashing the ancient dogma of "nature is afraid of vacuum" in scholasticism. He also studied the general law of liquid balance and found that "the pressure on the fluid in a closed container at any point is transmitted in all directions with the same intensity." This is the most basic principle in hydrostatics-Pascal principle.

Pascal is also a master of prose, thinker and theological debater. His Random Thoughts and Letters to Outsiders are listed as literary masterpieces. He used the ability of prose master to control words, and gave full play to the insights of thinkers. He is not only fluent in writing, but also famous for his sharp debate and profound thoughts. He had a great influence on the development of French prose, even on Voltaire, a great French writer.

However, when Pascal enjoyed a high reputation as a scientist, he often had nightmares at night because of weakness, indigestion, insomnia and headache. In particular, he was dominated by his world view, which made him gradually give up the discussion of mathematics and science and devote himself to religious meditation. After a few short years, although he returned to science, he was unable to concentrate. 1654 He once said: This updated scientific activity is not welcomed by God. This so-called divine revelation appeared after an accidental accident: once he was riding in a carriage, the horse went out of control over the railing of Naiqiao and fell into the river, but he was miraculously saved because the reins suddenly broke. He wrote the accident on a small piece of thick paper and kept it on his chest. He should firmly remember this revelation from now on. So he fatally returned to religious meditation. Pascal thought: "anything about faith can't be considered by reason." In the last period of his life, he even went to extremes, like an ascetic, wrapping a belt with spikes around his waist. If he thinks of any ungodliness, he will hit the belt with his elbow and sting his body. So he died at the age of 39. On his deathbed, he said in a weak voice, "May God be with me." Wolff, a famous British historian of science, said, "Pascal showed a precocious mathematical genius, but his activities in this field were hindered by religious scruples and ended in early death." Despite this, he has made remarkable progress in several different branches of mathematics and physics. "

Pascal thought: "A person's virtue must not be measured by his special efforts, but by his daily behavior." He also said: "Do you want people to praise you? Then don't flatter yourself, "he said. "Mathematics is the highest exercise for the spirit."