At that time, people found it inconvenient to calculate logarithms, especially some large numbers. In 2484, Qiu Kai and Yu Er studied hard to find a simple method to make the calculation of large numbers more convenient. Finally, they noticed the relationship between the following two series.
0， 1，2，3，4，5，6，7，8，9， 10，…
2 n 1，2，4，8， 16，32，64， 128，256，5 12， 1024，…
If the product of any two numbers in the second place is required, the corresponding answer can be found from the sum by calculating the number of the first line corresponding to these two numbers. If it is to display the main business, just change the "sum" above to "difference". Later, Steefel extended this relationship to negative exponent and fractional exponent.
Later, British mathematician Napier devoted himself to the study of spherics and division. With the rapid development of trigonometry, various trigonometric function tables appear in large numbers, which is the direct reason for his invention of logarithm. Because there was no decimal operation at that time, it was necessary to make tables for studying astronomy and navigation, and people could only meet the requirements of making tables by increasing the radius of the circle. Therefore, it is urgent to find a simple and effective calculation method for tabulation.
Napier's original purpose was to simplify some angle operations. When he saw the research results of Chukai and Steefel, he was enlightened. His idea is to follow the formula.
Sina sinB={cos(A-B)-cos(A+B)}/2
From here. He spent at least 20 years studying logarithmic theory.
Considering line AB and infinite ray DE, let point C and point F start from point A and point D at the same time and move along these two lines at the same initial speed. Assuming that c always moves at a speed equal to the distance CB and F moves at a constant speed, Napier defines d f as the logarithm of CB. That is, let df = x and CB = y,
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In order to avoid the trouble of fractions, Napier took the length of AB as 10 7, because the best positive table at that time had seven digits. In Napier's place, there is no concept of bottom. Starting from the continuous geometric quantity, he obtained the comparison table of geometric series and arithmetic series.
16 14, Napier published a wonderful logarithm theorem, in which he gave a lecture on logarithm. The book aroused widespread interest as soon as it was published. Later, when he and Briggs exchanged logarithms, the logarithm of 1 was 0, and the logarithm of 10 was an appropriate power of 10, so the logarithms table was more useful. So we have the common logarithm today. In memory of Briggs, people also call it Briggs logarithm. This logarithm is essentially based on 10, which is of great utility in numerical calculation.
1624, Briggs published his logarithmic arithmetic, which is a logarithmic table, including 14 common logarithms from 1 to 20000,90000 to 10000. Later, with the help of the publishing house, other figures ranging from 20,000 to 90,000 were added. 1620, Gunter, a colleague of Briggs, published a common logarithmic table of sine and tangent of angles, which was not replaced by the 20-bit logarithmic table calculated by Britain until 1930s and 40s.
The word logarithm means "logarithm". Napier did not use this word at first, but used artificialnumber (artificial number), and later used the word logarithm. In the hands of Briggs, the word mantissa was introduced, which means "addition" or "filling a vacancy". /kloc-in the 6th century, Briggs put forward the term logarithm.
The invention of Napier Logarithm and Briggs Logarithm Table was quickly recognized by people, especially in the field of astronomy. They thought that the invention of Logarithm prolonged the life of astronomers. Galileo even said that by giving him space, time and logarithm, he could create a universe.
Regarding the invention of logarithm, another person should be mentioned, that is, Bilgi, a Swiss instrument manufacturer. Bilgi is an assistant to astronomer Kepler. According to Steefel's findings, it took him eight years to raise a series of objections. Published in 1620, 6 years later than Napier.
Both Napier and bilkey devoted themselves to the study of logarithm, but Napier used geometric method and bilkey used algebraic method. Logarithm is now generally considered to be exponential. For example, n=b x, we can say that x is the logarithm of n based on b. From this definition, the law of logarithm comes directly from the law of exponent. The establishment of logarithm precedes the establishment of exponent, which has become a rare story in the history of mathematics.
All the above are logarithms based on 10, and there are natural logarithms. The name is 16 10, which appears in London mathematician speed's New Mathematics.
As we know, the base of a general logarithm can be any positive number that is not equal to 1. That is, if the base of a number is a transcendental number e(e=2.7 18), we call this logarithm a natural logarithm, which is represented by the symbol "LN". Here "1" is the first letter of logarithm, and "n" is the first letter of nature. When two letters are put together, it means natural logarithm.
The appearance of natural logarithm has brought a revolution to mathematics.
Number is a calculation method, and its greatest advantage is that the application of logarithm, multiplication and division can be simplified to simple addition and subtraction operations. Although the logarithmic table we are using now was invented by the famous Scottish mathematician Napier, it should be traced back to Chuckay and Steefel in 1484.
At that time, people calculated logarithms, especially some large numbers,