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# What are the Mathematics Achievements of the Mongolians?

The Mongolians have done a lot of research on mathematics. The first to study Euclid’s “Elements of Geometry” was Meng Ge. According to records, “The Genghis Khan kings Yimengge are more knowledgeable, and Bizhi explained some of the schemes of Euclid.”

In the early eighteenth century, Ming Antu, a Mongolian scientist who served at the Qintian Supervisor of the Qing Dynasty, made great contributions to mathematics. At that time, three analytic formulas related to trigonometric functions were imported from Europe, but they were not proved.

Mingan Tu “pity only has its method, but did not elaborate its meaning”, so he spent 30 years on research, not only created the “cut circle and connected proportion method” to prove three formulas, but also obtained six analysis independently. formula. The mathematics research manuscript left by Ming Antu was later compiled into a book by his son Ming Xin, students Chen Jixin, and Zhang Liangting, and was inscribed in a 4-volume mathematics monograph “The Method of Cutting the Circles, Secrets, and Shortcuts.”

“Circle cutting” refers to dividing the circumference into equal parts, or dividing the arc length in the circle into several equal parts, and then using the cutting circle method to find the circumference or the arc length in the circle.

This value is very close to the actual value, and it can also be said to be an approximation of the pi. “Quick method” refers to a method that can be easily and quickly calculated. In this book, he not only rigorously proved the correctness of the three infinite series passed in from the West, and deduced the three “circle diameter seeks the circumference”, “the arc back seeks the sine”, and “the arc back seeks the sine”. 6 formulas, and 6 infinite series were discovered and demonstrated, and 6 formulas that surpassed the world scientific level at that time were created, namely, the arc back seeks the string, the arc back seeks the vector, the string seeks the arc back, the sine seeks the arc back, The positive vector seeks the arc back, the vector seeks the arc back.

In proving these nine formulas, he created four formulas: cosine and cosine for cosine and sine, cosine and cosine for the original arc, sine and cosine by arc back, and sine and cosine for arc back by sine and cosine. The “method of cutting circles and connecting proportions” created by him contains the advanced ideas of the combination of figure and number and the mutual transformation of straight lines and arcs. This idea of ​​finding a circle with a straight line and finding a straight line with a circle has the same meaning as Western calculus. It was a relatively advanced idea in the world of mathematics at that time.

Therefore, Mingantu is regarded as the pioneer of calculus and the pioneer of advanced mathematics in our country, and has made significant contributions to the development of mathematics in our country.

The Mongolian people who study mathematics and have written works for later generations are not only Ming Antu alone, but also Dulun in the late Qing Dynasty. Du Lun authored a volume of “Yi Liao Da Fang Shu Cao”, also known as “Shao Guang Zhang Chu Bian”, the content belongs to elementary mathematics.

Cut circle ratio
It is the geometric basis of the series theory in the Qing Dynasty. It was first clarified by Ming Antu in “The Method of Cutting the Secret Rate and Shortcut”, and it was later improved by the work of mathematicians such as Xiang Mingda and Dong Youcheng. . The central problem of cutting circle connection ratio is how to find the length of the arc when the arc length is known, how to find the length of the chord and the height of the vector, or how to find the length of the arc when the length of the chord and the height of the vector are known.

The method of cutting the circle and connecting the center of the proportion is to combine the method of connecting the proportion introduced from the West and the traditional Chinese calculation method to divide the arc into multiple equal parts, draw multiple vectors, and then construct a series of similar triangles to obtain a series of continuous proportions. , And then divide the arc to be thinner, and use a broken line to approach the arc to obtain the arc length.

Mingantu also proposed four formulas that use cosines, cosines, and cosines to simplify calculations with the help of trigonometric transformations. At the same time, it also solves the calculations of cosines and arccosines. Volume 2 “Usage” is the use of each formula in mathematics and astronomy Application examples include the calculation of trigonometric function values ​​such as sine and cosine, the solution of plane and spherical triangles, the calculation and conversion of the right ascension, declination and yellow longitude of Venus, and the calculation and conversion of yellow latitude.