What kind of person is Pascal and what kind of scholar is he?

Pascal was a famous French mathematician, physicist, philosopher and essayist.

He was born on June 19, 1623 in Clermont-Ferrand, Dome Hill Province, France. Pascal did not receive formal school education. His mother died of illness when he was 4 years old. His father and two sisters, who were highly educated and served as government officials, were responsible for his education and training. His father was a respected mathematician. , under his careful education, Pascal became proficient in Euclidean geometry at a very young age. He independently discovered the first 32 theorems of Euclid, and the order was completely correct. At the age of 12, he discovered "the interior angles of a triangle" alone. After "The sum is equal to 180 degrees", he began to study mathematics with his father. In 1631, Pascal moved to Paris with his family. His father found that Pascal was very promising. When he was 16 years old, he took him to join the group of Parisian mathematicians and physicists ( The academic activities of the French Academy of Sciences in Paris (the predecessor of the Paris Academy of Sciences) opened his eyes. When he was 17 years old, Pascal wrote the article "The Theory of Conic Sections" with a high level of mathematics. This was his study of De Zalgue's classic work on synthetic projective geometry. As a result.

In 1641, Pascal moved to Rouen with his family. While helping his father in tax calculations from 1642 to 1644, Pascal invented the adding machine, the earliest calculator in the world, which is now on display at In the French Museum. In 1610, he accepted religious teachings, but was still committed to scientific experimental activities. Between 1653 and 1653, Pascal concentrated on research on vacuum and hydrostatics, and achieved a series of major results. Returned in 1647 Living in Paris. He conducted a large number of experiments based on Torricelli's theory. The experiment in 1647 shocked the whole of Paris. He himself said: The fundamental guiding idea of ??his experiments is to oppose the traditional concept of "nature abhors a vacuum". 1647 From 1648 to 1648, he published a paper on the vacuum problem. In 1648, Pascal conceived and conducted an experiment to measure the atmospheric pressure at different heights in the same area, and discovered the law that the atmospheric pressure increases as the altitude decreases. In these years During the period, Pascal continued to make new discoveries in experiments, and made many major inventions, such as the invention of the syringe, the hydraulic press, and the improvement of Torricelli's mercury barometer. From 1649 to 1651, Pascal and his collaborator Pi Perier measured the changes in atmospheric pressure at the same location in detail and became a pioneer in using barometers for weather forecasting. In 1651, Pascal began to summarize the results of his experiments, and by 1654 he wrote "Essays on the Balance of Liquids and the Weight of Air." It was officially published in 1663. After that, Pascal turned to theological research, and in 1655 he entered the theological center Pitreira. He started from skepticism and believed that both perceptual and rational knowledge were unreliable, and thus came to the conclusion that faith is above all else.

Before 1646, Pascal's family all believed in Catholicism. Due to his father's illness, he came into contact with a more profound way of religious belief, which had a great influence on his future life. Pascal and mathematicians Fermat correspondence, they worked together to solve a problem sent by a certain upper-class gambler and amateur philosopher. He couldn't figure out why he always lost money when he bet on a certain combination of three dice. After they solved this problem In the process, he laid the foundation of modern probability theory. In his short life, he made many contributions, with the greatest contribution in mathematics and physics. In 1646, he tested the Italian physicists Galileo and Torricelli. theory, made a mercury barometer, and repeatedly conducted atmospheric pressure experiments on the top of Clermont-Ferrand overlooking Paris, paving the way for the study of fluid dynamics and hydrostatics. During the experiments, he tried to improve Torricelli's pneumatic juice, he invented the syringe and created the hydraulic press based on Pascal's law. His research and writings on vacuum issues further enhanced his reputation. He was physically weak since he was a child and suffered from overwork. However, it was during his sick leave from 1651 to 1654 that he intensively carried out scientific work and wrote many papers on liquid balance, the weight and density of air, and arithmetic triangles. The latter paper became the basis of probability theory. Basics.In 1655

~1659, he also wrote many religious works. In his later years, someone suggested that he publish the results of his research on tricycles, so he immersed himself in scientific interests. However, from February 1659, his illness worsened and he could not He worked normally and settled into a pious religious life. Finally, he died of great illness.

Pascal passed away on August 19, 1662, at the age of 39. Later generations used his name in memory of Pascal. To name the unit of pressure, referred to as "Pascal".

Research fields

Pascal's achievements are multifaceted. His contributions to mathematics and physics have made great contributions to science. It occupies an extremely important position in history.

Pascal's mathematical attainments are very profound. In addition to his outstanding contributions to probability theory and other aspects, the most outstanding one is the famous Pascal's theorem-his paper on conic sections "Pascal's theorem proposed in "Pascal's theorem" is an important theorem of projective geometry, that is, "the line of intersection of the three pairs of sides of a conic inscribed in a hexagon".

In algebra research, he published He wrote many papers on arithmetic series and binomial coefficients, and discovered the coefficient rules of binomial expansions, which is the famous "Pascal's triangle" (called "Yang Hui's triangle" in our country). He and Fermat ** * also established the basis of probability theory and combinatorial theory, and derived a series of solutions to probability theory problems. He studied the cycloid problem and derived general methods for finding the areas and centers of gravity of different curves. He calculated trigonometric functions and The integral of the tangent was the first to introduce the elliptic integral.

Research contributions

1. In 1639, he published an excellent mathematical paper "On Conic Sections"

2. He wrote the famous philosophical work "Thoughts"

3. Pascal discovered the law that atmospheric pressure increases with altitude. He not only repeated Torricelli's experiment, but also verified his own inference : Since the atmospheric pressure is generated by the weight of the air, the higher the altitude, the shorter the liquid column in the glass tube.

4. "Letter to Foreigners"

5. In 1641, Pascal invented the adding machine

6. "A Treatise on Conic Sections"

7. Discovered Pascal's law (in fluid (gas or liquid) mechanics, Refers to the pressure change that occurs in a certain part of the stationary fluid in a closed container, which will be transmitted to all parts of the fluid and the container wall without loss. The pressure is equal to the acting force divided by the acting area. According to Pascal's principle, on a piston in a hydraulic system Applying a certain pressure will produce the same pressure increase on the other piston. If the area of ??the second piston is 10 times the area of ??the first piston, then the force acting on the second piston will increase is 10 times that of the first piston, while the pressure on the two pistons is still equal. The hydraulic press is an example of Pascal's principle. It has many uses, such as hydraulic braking, etc.

8. Pascal also discovered : The pressure at any point in a stationary fluid is equal in all directions, that is, the pressure at that point is equal on all planes passing through it. This fact is also called Pascal's principle (law).

About physics Interlude

There is such a joke: after death, scientists all go to heaven. One day, the scientists were playing hide-and-seek, and it was Einstein’s turn to catch them. After he counted 100, he found that Newton stood When you are around, say: "Newton, I caught you."

"No, you are not catching Newton."

"Then who are you?" Einstein Asked.

"What do you see under my feet?" Newton smiled slyly.

Einstein saw that under Newton's feet was a square wooden board with a side length of one meter.

"I stand on a square meter of wood, which is 'Newton/square meter', so what you catch is not Newton, but 'Pascal'①."

Einstein After hearing this, he called Pascal. After hearing this, Pascal smiled, bent down, picked up the board at Newton's feet and said to Einstein: "I am Pascal now, right?" After that, he threw the board away.

Go out. "There are no square meters, now, I am Newton."

① If you don't understand, see Pressure