In the fields of mathematics and physical mathematics, Bernoulli can be seen everywhere, such as Bernoulli series, Bernoulli-Leibniz paradox and Bernoulli equation.
In the history of mathematics, there is a difficult problem that has been solved for more than two thousand years. The form of this problem is very simple: find the sum of natural number 1, 2, 3, and all the way to any power (natural number power). To write a formula is to find sk 1k+2k+3k+...+NK, where k is a natural number.
When K= 1, the Pythagorean school in the 6th century BC found the answer, that is, S 1 = 1+2+3+...+n, and then s \-1=1/2 (n+6550 In 1 century, Nikumak solved S3, while S4 was not solved by Arab mathematicians until 1000.
For any natural number K, it was17th century Jacob Bernoulli who completely solved this problem.
Jacob Bernoulli was born in 1655 and is a descendant of Bernoulli family. Nearly half of the people in this family are talented, and almost all of them are outstanding scholars, professors, politicians and artists. This family plays a prominent role in the development of calculus theory. They have made family contributions to the development of modern mathematics.
The Bernoulli family live in the Netherlands. They believe in Protestantism. Therefore, they were persecuted by the Catholic Church. 1583, in order to escape the Catholic massacre and cruel persecution, Bernoulli's family moved to Switzerland and settled in the famous city of Basel. As soon as he moved to Basel, he became in-laws with a local rich businessman. Ancestor Nicolaus Bernoulli married the daughter of a wealthy businessman, and later became one of the important members of the aristocratic group that ruled the whole Basel merchant.
Jacob Bernoulli is the second generation of this family who moved to Basel. His two younger brothers are Nicholas I and John I. The three of them have made extraordinary contributions to calculus and enjoyed a high reputation. At the end of 17, Jacob Bernoulli developed Leibniz calculus, founded the variational method, and put forward and solved some isoperimetric and tangent problems.
According to incomplete statistics, among the 12 grandchildren of Bernoulli family, there are at least 10 mathematicians.
Jacob Bernoulli also put forward a famous topic in middle school mathematics, if the first two items of a arithmetic progression are the first month. Different from each other, and these two items are the same as the first two items of a geometric progression, then all the subsequent items of this geometric progression are smaller than the corresponding geometric progression.
Jacob Bernoulli is also called the first Jacob. He was smart and diligent since childhood, taught himself Descartes' works, and later met famous mathematicians such as Leibniz and Huygens.
Mathematicians of Bernoulli family started from Jacob, and most of them were professors of mathematics in university of basel. 1686, Jacob became the first professor of university of basel in the Benuri family. He studied the catenary problem in detail and thoroughly. Jacob Bernoulli proved that if both ends of a given length of rope are suspended, the center of gravity of the catenary is the lowest. The current application principle of suspension bridge and high voltage transmission line comes from this.
Jacob's first epitaph was engraved with two logarithmic spirals, one reverse and the other positive, which he discovered in his later years. No matter whether the logarithmic spiral is enlarged or contracted, its shape will not change as long as its position changes. So the inscription reads "Although I change, I will still achieve it".
Jacob Bernoulli's younger brothers Nicholas and John are both mathematicians. Nicholas later studied mathematics in St. Petersburg. When he died, Queen Catherine gave him a state funeral. John took over from his brother, 1705, a professor of mathematics in university of basel. Euler grew up under the guidance and education of John.
John is a mathematician and plays an important role in calculus. The famous problem that Newton solved in his later years was written by John. John, Jacob, Leibniz, lobita, Newton and others worked hard to solve the "steepest descent line" and became the researchers of early variational science.
Several mathematicians of Bernoulli family began to study medicine, law and philosophy, got the highest degree, and then turned to mathematics. Where are their hobbies? Their family is a typical family of natural science scholars.
John's son is Daniel. He was born in Groningen, the Netherlands.
In 1695, Leibniz pointed out that force should be divided into "dead force" and "vitality", in which "dead force" refers to static force and "vitality" refers to dynamic force. Leibniz's viewpoint has a great influence, and daniel bernoulli published Fluid Dynamics in 1738. In this book, the method of calculus is applied to the study of fluid dynamics and gas dynamics, and a theoretical system is established, which is Bernoulli equation, also known as Bernoulli principle.
Daniel is the pioneer and founder of mathematical physics methods.
Daniel's younger brother John's second and several cousins are also mathematicians.
Bernoulli family is a famous family in Sweden and even Europe. Later, they worked in Petersburg Academy of Sciences and recommended Euler.
The principle of virtual work was put forward by John in the second discussion with Daniel and recorded in the Letters between Father and Son.