Bai: All astronomers should thank mathematics discovery

The following article comes from WeChat public account: Hui Pu, author Richard Elwes

For centuries, both scientists and engineers have been very practical tools. Now, due to the close connection with the index function, the number of mathematics is still full of mathematics.

Written article | Richard Elwes (Richard Elwes)

Translation | Qi Ruihong, Fang Chao, Yu Mi

In the past many years, many people have been used to putting the table table at hand to help themselves and dividends. In the second half of the 20th century, the portable calculator eventually pushed the number table into history. However, in the field of deep mathematics in the level and calculus, the fascinating discovery ensures that the number itself is never outdated.

In the late 16th century, John Napier began to study the number of "artificial numbers" originally called "artificial number". He discovered a method that can transform complex multiplication operations into quite simple plus operations. In order to find the product of two numbers, such as 4587 and 1962, he first calculated the artificial number of these two numbers and found them. Then the two artificial numbers and anti -artificial numbers are calculated, that is, the calculation of the original number so that its artificial number is this harmony. Although this process does not involve multiplication operations, the result of the obtained is indeed the product of the two numbers -899 694.

The seismic meters are used to measure the intensity of the earthquake. The Risiti seismic table that measures the intensity of the earthquake, the internationally universal is the calculation of numbers: the seismic intensity measured as a magnitude 3 is 10 times that of the seismic intensity measured to magnitude 2.

Nippier's pair

Soon after, Nipil gave him a new, better name -pair. Today, we understand that the pairing number is just the counterattack calculation. Mito transportation refers to a certain number of repeated multiplications with it. Therefore, "2 of 2" refers to 3 multiplications, that is, 2 × 2 × 2 = 8, or 23 = 8. Correspondingly, we say "with 2 as the bottom, the number of 8 is 3", which is recorded as log28 = 3. You can use any number as the bottom number to get the number, for example: 10 as the bottom, the number of 1000 pairs is 3 (because 10 × 10 × 10 = 103). For Nipil's multiplication, the entire calculation process needs to determine a bottom number. Therefore, calculate 8 multiplied with 64, first take 2 as the bottom number, and obtain 3 and 6 respectively. The last step is the calculation process of the calculation process, that is, calculate 29 = 512 (you can check 8 × 64 = 512).

Briggs's pair table

Shortly after John Nipil invented, Henry Briggs began to transform it into a useful tool. Because we applied the decimal number system to indicate the number, Briggs chose to calculate the pair with 10 as the bottom, and began to make a "pair table" -the number of all integers from 1 to 1000. For a few years, Britz and other mathematicians have promoted this table to a larger number.

Of course, for most integers, their pairs are not integer, so researchers have to give the accuracy of the number they get. In the late 18th century, Gaspard de Prony supervised and produced a special mathematical watch. This mathematical table was as many as 17 large -scale dual -opening volumes, including the upper and 200,000 positive integer pairs. Digital, accurate to the 19th place after decimal point (for larger numbers, accurate to 24th place).

It was taken from John Nipil's earliest monograph "The Description of the Wonderful Table" in 1614. John Nipil studied the number of "natural pairs" later, while Henry Bridis studied the pair with 10 as the bottom -later called "commonly used numbers".

Natural logarithm

Nippel has been very useful for mathematicians since its discovery. As an outstanding scientist Pierre-Simon Laplace says: "Discover the life of the number by saving the life of a astronomer." It is more important and far -reaching as a computing tool. In 1650, Pietro Mengoli realized this for the first time. The study of his relevant level is unexpectedly combined with his interest in numbers.

The expression of harmony level is

Essence Mansoli noticed that this expression was not approaching any limited number, but did not continue to increase in the upper limit. However, if you modify it slightly, another expression you get 1-

Convergence in a fixed number.

This staggered level has a certain limit, which is about 0.693147. Mandari proves that this limit is the number of nature 2 (usually recorded as IN2, although read as log2). Naturally, the number is like any other pair, but there is a special choice for the bottom number. E -E as the bottom number, E is equal to 2.71828. Indeed, it is through the conclusions of nature and Mansoli that one of the most important functions in mathematics, the index function, began to emerge.

Indeed, the search for more accurate number tables has effectively promoted the development of abstract number theory. In 1668, Nikolaus Mercator published a book called "Division Technology". In this book, he found the natural pair of number formula: this beautiful theory is Mansoli, Mandari The promotion of the result, the result of Mangoli corresponds to the special situation of x = 1.

Plugs and numbers

Makato's theorem implies the "nature" of nature, but a more complete story needs to use Newton and Leibnitz's calculus theory.

equation

Describe an important concept called "countdown". It is this equation that connects 2 and 方, 4 and ¼, one million and one millionth. From a geometric figure, it is a curve called "dual curve". Unexpectedly, the statement of "natural pairing as the area below this curve" appeared. This is also a conclusion of the fact that the number of the number function is the reverse function of the index function. As a result, the number of guidance of the number y = inx can only be a function

Essence Although the number table has been replaced by the computer, this profound fact ensures that the number of numbers still play an important role in mathematics.

This article is authorized to be excerpted from the 26th "Mathematical Breakthrough in Mathematics: Mathematical Mathematics: The Mathematical World".

This article is reproduced from WeChat public account: Returne author: Richard Elwes

Reprinted content only represents the author's point of view

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It does not represent the high energy office of the Chinese Academy of Sciences

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