Jacob Bernoulli

Swiss mathematician

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Jacob Bernoulli (Jakob Bernoulli, 1654-1705), Bernoulli Family One of the representatives, Switzerland mathematician. Recognized probability theory One of the pioneers of. He was the first to use“ integral ”People who use this term also use it earlier Polar coordinate system One of the mathematicians of. It was also stated earlier that as the number of tests increased, Frequency stability Near the probability. He also studied catenary The equation of isochronous curve is also determined. In probability theory Bernoulli test And Theorem of large numbers It was also put forward by him.^[1]

Chinese name: Jacob Bernoulli
Foreign name: Jakob Bernoulli‎
Nationality: Switzerland
date of birth: December 27, 1654
Date of death: August 16, 1705
University one is graduated from: University of Basel

Occupation: mathematician
Key achievements: Solving catenary problems
Curvature radius formula
Isoperimetric problem
one's native heath: Basel
Representative works: The Method of Qualifying the Area of a Triangle with Two Perpendicular Lines

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Jacob Bernoulli

Jacob Bernoulli was born on December 27, 1654 Basel, Switzerland , died at the same place on August 16, 1705. Jacob Bernoulli was born in a merchant family. He graduated from the University of Basel and obtained a master's degree in art in 1671. Later, he obtained a master's degree in theology at his father's will. However, he ignored his father's objection and taught himself mathematics and astronomy. Jacob Bernoulli traveled to Europe twice in 1678 and 1681 to study and travel, making him contact with many mathematicians and scientists, enriching his knowledge and broadening his interests. He returned in 1682 Basel And began to teach mechanics. In 1687, Jacob became a professor of mathematics at the University of Basel. Until his death, he had been in charge of the chair of mathematics at the University of Basel. In addition to doing mathematical research, he also made many friends, wrote voluminous letters, and was an influential figure in European scientific circles at that time.

Character's Life

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Christian Huygens

Jacob Bernoulli was born in Basel on December 27, 1654 and graduated from the University of Basel. In 1671, he received a master's degree in art at the age of 17. Art here refers to "free art", including arithmetic geometry , astronomy, mathematical music, grammar, rhetoric, and oratory. In accordance with his father's wishes, he obtained a master's degree in theology at the age of 22 in 1676. However, he also went against his father's wishes and taught himself mathematics and astronomy. In 1676, he arrived Geneva do private tutor 。 From 1677, he began to write a rich "Meditation Record" there.

In 1678 and 1681, Jacob Bernoulli went on two trips to study in France Netherlands , Britain and Germany, contacted and communicated with Xu De, Boyle, Hooke Huygens And other scientists who wrote about the comet theory (1682) Gravity theory (1683). In 1687, Jacob published his mathematical paper "The Method of Qualifying the Area of a Triangle with Two Perpendicular Straight Lines" on the Journal of Teachers. In the same year, he became a professor of mathematics at the University of Basel until his death on August 16, 1705.

In 1699, Jacob was elected as a foreign academician of the Paris Academy of Sciences; In 1701, it was approved by the Berlin Science Association (later Berlin Academy ）Admitted as a member. Many mathematical achievements are associated with Jacob's name. for example catenary Question (1690), Radius of curvature Formula (1694)“ Bernoulli double newcastle line ”(1694)“ Bernoulli differential equation ”(1695)“ Isoperimetric problem ”(1700), etc.

Jacob's greatest contribution to mathematics is probability theory Research. Since 1685, he has published Gambling game The paper on the number of wins and losses was later written into a masterpiece《 Guesswork 》This book was published in 1713, 8 years after his death.

Logarithmic spiral

One of the most interesting anecdotes is Jacob's devotion to the study of logarithmic spiral, which began in 1691. He found that after various transformations, the logarithmic spiral is still a logarithmic spiral, such as its Evolute and Evolute Is a logarithmic spiral from pole to pole tangent The trajectory of the vertical foot of Reflection ray , as well as the curve (echo line) tangent to all these reflection rays Logarithmic spiral 。 He marveled at the magic of this curve, and asked future generations to carve logarithmic spiral on their tombstones in their wills, with the eulogy "Even if changes, still be me", to symbolize immortality after death.

Jacob Bernoulli

The 22nd session in 1994 International Congress of Mathematicians stay Switzerland Of Zurich Convene, Swiss Post Issued Commemorative Stamp Of Stamp pattern It's the head of Jacob Bernoulli, named after him Law of large numbers And the geometry of the law of large numbers Sketch Map (i.e. when the number of tests increases infinitely Frequency stability In its probability of occurrence) Bernoulli Family It is a Swiss family that once produced 11 scientists, Jacobian ·Bernoulli is one of the important members, and has made many significant achievements in mathematics For example, he once told Calculus Has made important contributions to the development of; by ordinary differential equation Of integration method Lay a theoretical foundation; In the study of curve problems, he proposed a series of new concepts; He founded Variational method ； He is also an early researcher and founder of probability theory

Mathematical family

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It is worth mentioning that the Bernoulli family is a family of mathematicians. In addition to Jacob Bernoulli, there were 11 mathematicians in the Bernoulli family during the 17th - 18th century. Among them, his younger brother John Bernoulli (1667 - 1748) and nephew Daniel Bernoulli (1700 - 1782) were more famous, and they were introduced into probability theory Normal distribution Error theory, published the first normal distribution table). Jacob Bernoulli is the first member of the Bernoulli family Mathematical research People who become famous.

Key achievements

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Jacob Bernoulli's contribution to mathematics involves calculus differential equation 、 Infinite series Summation analytic geometry , probability theory and variational method. Jacob Bernoulli's most outstanding contribution to mathematics is in the fields of probability theory and variational method. His theory of probability Work achievements Included in his paper The Art of Speculation. In this book, he made several important contributions to probability theory, including the discovery of what is now called the law of large numbers. This paper also records Jacob Bernoulli's argument Permutation and combination Work. People in the Bernoulli family always like to argue on academic issues. Looking for Fastest descent line , that is, under the independent action of gravity, a particle passes through two fixed points Shortest path Jacob Bernoulli and his brother John Bernoulli had a heated debate on the issue of. The result of this serious debate is the variational method. In addition, Jacob Bernoulli also made important contributions to the study of catenary, and he also used the results in this regard in the design of bridges. In 1694, he first gave Cartesian coordinates and polar coordinates This is also the beginning of systematic use of polar coordinates. Jacob Bernoulli and his brother John Bernoulli developed and spread the idea that Newton and Leibniz had just invented Calculus Played an important role in the creation of calculus. Jacob Bernoulli's special contribution to calculus is that he pointed out how to apply this technology to applied mathematics The word "integral" was first used by him in 1690.

Jacob Bernoulli's most creative book in his life was The Art of Guessing published in 1713 Combinatorial mathematics And a major event in the history of probability theory Bernoulli number There are many applications. In probability theory“ Bernoulli theorem ”This is the earliest form of the law of large numbers Because the Bernoulli brothers scientific problems The over heated debate on led to the involvement of the families of both sides, so that after the death of Jacob Bernoulli, his manuscript of "The Art of Guessing" was hidden by his widow and son for many years, and it was not published until 1713, almost damaging the value of this classic work. Due to the extreme importance of the Law of Large Numbers, December 1913 Petersburg Academy of Sciences A celebration meeting was held to commemorate the 200th anniversary of the birth of the Law of Large Numbers.

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