Galileo also said, "Give me space, time and logarithm, and I can create a universe."
Before the invention of logarithm, people were familiar with the method of converting the product of trigonometric functions into the sum or difference of trigonometric functions. German mathematician M.Stifel (about 1487- 1567) expounded the following correspondence in Comprehensive Arithmetic (1544):
This relationship can be summarized as follows
At the same time, the operational nature of this relationship (that is, the multiplication, division, power and root of the upper row number correspond to the addition, subtraction, multiplication and division of the lower row number) has also been widely known. After years of research on the operation system, Napier published the Explanation of the Wonderful Logarithm Law in 16 14, in which the logarithmic method was expounded in geometric terms with the help of kinematics.
It was Napier's friend H.Briggs (1561-1631) who transformed the logarithm and made it widely spread. He found it inconvenient to use logarithms by studying the Handbook of Wonderful Logarithm Law, so he agreed with Napier to set logarithms as 1. Because our number system is decimal, we have an advantage in numerical calculation. 1624, Briggs published logarithmic arithmetic, and published 1~20000 and 90000 ~ 10000 as the cardinal numbers.
According to the principle of logarithmic operation, people also invented the logarithmic slide rule. For more than 300 years, the logarithmic slide rule has been an indispensable computing tool for scientists, especially engineers and technicians. It was not until the 1970s that it gave way to electronic calculators. Although the logarithmic slide rule and logarithmic table are no longer important as a calculation tool, the logarithmic thinking method still has vitality.
From the process of logarithmic invention, we can find that Napier did not use the reciprocal relationship between exponent and logarithm when discussing the concept of logarithm. The main reason for this situation is that there was no clear concept of exponent at that time, and even the exponent symbol was written by French mathematician Descartes (R.Descartes, 1596- 1650) more than 20 years later. It was not until the18th century that the Swiss mathematician Euler discovered the reciprocal relationship between exponent and logarithm. In a book published by 1770, Euler first used it.
To define
He pointed out: "Logarithm originates from exponent". The invention of logarithm preceded exponent and became a rare story in the history of mathematics.
From the process of logarithmic invention, we can see that the needs of social production and science and technology are the main driving force for the development of mathematics. The process of establishing the relationship between logarithm and exponent shows that it is very important to use a good symbol system for the development of mathematics. In fact, good mathematical symbols can greatly save people's thinking burden. Mathematicians have made long and arduous efforts to develop and improve the mathematical symbol system.
Common Strategies for Solving Logarithmic Functions