Binomial theorem occupies a very important position in modern mathematics, and it is also an important test point of college entrance examination. Every year, the college entrance examination will focus on such questions.
The definition of binomial theorem can be simply described as: expanding the "arbitrary real power" of the "sum of two numbers" into the form of "sum"
This important theorem was founded by Newton in 1664 on the basis of previous research results. It has been 1500 years since its embryonic form was put forward and formally established. Countless mathematicians have worked hard for this.
Pay tribute to the great mathematicians who have made outstanding contributions to human civilization!
In 263 AD, the prototype of binomial theorem appeared in China's ancient mathematical masterpiece Nine Chapters Arithmetic.
How important is binomial theorem? You may not think of it.
Our ancestors recorded the "square root" and "square root" of "multiple positive integers" in distant ancient times, much earlier than in the West.
1050, Jia Xian, a mathematician in the Northern Song Dynasty, completed the mathematical work Nine Chapters of the Yellow Emperor, Fine Grass. Unfortunately, it has been lost, and only a part of it has been passed down to future generations.
200 years later, in 126 1 year, some contents in the book, such as "Jia Xian Triangle" and "Methods of Increasing, Multiplying and Opening", were copied into the famous "Yang Hui Algorithm" by famous mathematicians in the Southern Song Dynasty, which spread all over the world and was also called "Yang Hui Triangle" in the mathematical field, making important contributions to the development of human mathematics.
How important is binomial theorem? You may not think of it.
Unfortunately, China's ancient mathematical research did not form a systematic theory. Although there is the rudiment of binomial coefficient, the general formula of binomial coefficient is not further summarized.
It can be seen that China's ancient mathematics focused on "independent application of problems" and did not form an "axiomatic system" of mathematical thinking.
In the west16th century, "binomial coefficient table" has been deeply rooted in people's hearts and appeared in many mathematicians' works.
1654, the mathematician Pascal established the binomial theorem of "general positive integer power".
Through the efforts of countless mathematicians, the "binomial theorem" has gone through the long river of years and experienced storms, and finally came out perfectly.
1665, Newton founded the modern binomial theorem on the basis of previous research results.
How important is binomial theorem? You may not think of it.
100 years later, mathematicians Euler and Geoffrey Castillion proved this point strictly by mathematical induction.
At this point, the great binomial theorem was born!
Binomial theorem and Yang Hui triangle are amazing combinations of numbers and shapes in the history of mathematics.
The problem of binomial expansion coefficient is actually the calculation of combination number, and the combination number can be obtained quickly by using Yang Hui triangle number.
Binomial expansion is closely related to Yang Hui's triangle number. Calculation with "general formula of coefficient" is called "formula calculation"; Using "Yang Hui triangle" to calculate is called "graphic calculation".
How important is binomial theorem? You may not think of it.
The same result, the same road, the beauty of mathematics, magic!
Binomial theorem plays an important role in combinatorial theory, higher power, higher arithmetic progression sum difference method.
Most importantly, the continuous improvement of binomial theorem has laid a solid foundation for the establishment of calculus and played a vital role in promoting the development of human science and technology.
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