The early trigonometry was not an independent discipline, but attached to astronomy, which was a method to calculate astronomical observation results. Therefore, it was first developed in sphericity. Mathematics in Greece, India and * * * all contain trigonometry, but most of them are by-products of astronomical observation. Measuring the distance between celestial bodies is not an easy task. Astronomers divide the celestial bodies that need to be measured into several grades according to the distance. Celestial bodies close to us, they are not more than 65,438+000 light years away (65,438+0 light years = 9.46 trillion 65,438+0,065,438+02 kilometers). Astronomers use the triangle parallax method to measure their distance. Triangular parallax method is to put the celestial body to be measured on the vertex of a super-large triangle, and the two ends of the diameter of the earth's orbit around the sun are the other two vertices of this triangle. By measuring the angle of view of the earth to that celestial body and using the known diameter of the earth's orbit around the sun, we can calculate the distance from that celestial body to us through the trigonometric formula. We can't measure the distance between celestial bodies and the earth by the triangle parallax method, because their parallax can't be accurately measured on the earth. [The distance between celestial bodies in Hanoi is also called parallax, the opening angle of the average distance (a) from the sun to the earth is called the triangular parallax (p) of the star, and the distance d near the star can be expressed as sin π.
If π is very small, π is expressed in angular seconds and the unit is parsec (pc), then D= 1/π.
Measuring the distance between stars with annual parallax method has some limitations, because the farther away the stars are from us, the smaller π is, which is difficult to measure in actual observation. Triangular parallax is the basis of distance measurement of all celestial bodies. So far, more than 65,438+00,000 stars have been measured by this method. So trigonometry was derived from astronomy, which laid the foundation for astronomical research.
Trigonometry originated in ancient Greece. In order to predict the running route of celestial bodies, calculate the calendar, navigate and other needs, the ancient Greeks studied the relationship between the angles of a spherical triangle, and mastered the theorems that the sum of two sides of a spherical triangle is greater than the third side, the sum of the internal angles of a spherical triangle is greater than two right angles, and the angles are equal. Indians and Indians also studied and popularized trigonometry. However, it is mainly used in astronomy. In the 15 and 16 centuries, the study of trigonometry shifted to the plane triangle to achieve the purpose of measurement application. /kloc-In the 6th century, the French mathematician Veda systematically studied the plane triangle. He published a book about the mathematical laws applied to triangles. From then on, the plane triangle was separated from astronomy and became an independent branch. The content of plane trigonometry mainly includes trigonometric functions.
The development of trigonometry is very long.
Menelaus of Alexandria first wrote "The Science of the Ball", and put forward the basic problems and concepts of trigonometry, especially Menelaus theorem of the ball science. Fifty years later, another ancient Greek scholar Ptolemy wrote Astronomy, which initially developed trigonometry. In 499 AD, Indian mathematician Ayabata also expressed the trigonometric thought of ancient India. Then Varahamihira first introduced the concept of sine and gave the earliest sine table. Some scholars in 10 century further explored trigonometry. Of course, all this work is an integral part of astronomical research. It was not until Nasir-ud-Deen (1201~1274) that trigonometry began to break away from astronomy and become a science. Reggiomontanus, 1436~ 1476).
Reggio Montanus' main work is to study triangles, which was completed in 1464. This is the first trigonometry work in Europe that is independent of astronomy. The book consists of five volumes. The first two volumes discuss plane trigonometry and the last three volumes discuss sphericity, which is the source of trigonometry spread in Europe. Reggio Montanus also made some trigonometric tables earlier.
The work of Reggio Montanus laid a solid foundation for the application of trigonometry in plane and spherical geometry. After his death, his manuscripts were widely circulated among scholars and finally published, which had a considerable impact on mathematicians in the16th century, and also had a direct or indirect impact on a group of astronomers such as Copernicus.
The word trigonometry was first used by the Renaissance German mathematician Pittis Qiusi (B. Pitiscus,1561613), who published Trigonometry: A Concise Solution to Triangle in 1595. Its composition method is composed of triangles.
Triangulation also appeared very early in China, and it was explained in detail in Classic of Weekly Parallel Computing, which was over 0/00 years BC. For example, the first chapter of it records "Duke of Zhou said", so you should use the method of moment. "Shang Gao said," The flat moment is tied with a positive rope, the flat moment is held high, the complex moment is deep, and the lying moment is far away. "(Shang Gao said, moment is used by present people.
The Austrian mathematician Rhaticus (G.J. Rhetucus, 15 14 ~ 1574) was the first to make trigonometric function tables in16th century. He graduated from Wittenberg University in 1536 and stayed there to teach arithmetic and geometry. For the first time, Rhaticus compiled tables of all six trigonometric functions, including the first detailed tangent table and the first printed secant table.
/kloc-After the invention of logarithm in the 7th century, the calculation of trigonometric function was greatly simplified. It is no longer difficult to make trigonometric function tables, and people's attention has turned to the theoretical research of trigonometry. However, the application of trigonometric function table has always occupied an important position and played an irreplaceable role in scientific research and production and life.
The triangle formula is the relationship between sides and angles, or the relationship between sides and angles of a triangle. The definition of trigonometric function has embodied certain relations, and some simple relations have been studied by the ancient Greeks and later people.
In the late Renaissance, French mathematician F. Vieta became a master of trigonometric formulas. His Mathematical Laws Applied to Triangles (1579) is one of the earliest monographs that systematically discussed planes and spheres. The first part lists six kinds of trigonometric function tables, some of which are separated by fractions and degrees, and gives trigonometric function values accurate to 5 digits and 10 digits. There are also multiplication tables and quotient tables related to triangular values. In the second part, the method of making the table is given, and the calculation formula of the relationship between river streamlines in the triangle is explained. In addition to summarizing predecessors' achievements, I also added my own new formulas, such as tangent law and sum-difference product formula. He listed these formulas in a general table, so that after giving some known quantities at will, the values of unknown quantities can be obtained from the table. This book is based on a right triangle. Vedas imitate the methods of the ancients and transform them into right triangles. For spherical right triangle, a complete calculation formula and its memory rules, such as cosine theorem, are given. 159 1 year Veda got the polygon relation, 1593 deduced the cosine theorem by triangle method.
1722, the British mathematician A. de moivre got the trigonometry theorem named after him.
? (cosθ isinθ)n=cosnθ+isinnθ，
It is proved that this formula holds when n is a positive rational number. In 1748, L. Euler proved that the formula also holds when n is an arbitrary real number, and he also gave another famous formula.
? eiθ= cosθ+isθ，
It has played an important role in promoting the development of trigonometry.
Modern trigonometry began with Euler's introduction to infinite analysis. He defined the unit circle and trigonometric function by the ratio of function line to radius. He also created lowercase Latin letters A, B and C to represent the three sides of a triangle, and uppercase Latin letters A, B and C to represent the three angles of a triangle, thus simplifying the triangle formula, and further transforming trigonometry from studying triangle solutions to studying trigonometric functions and their applications, becoming a relatively complete branch of mathematics.
Now people understand trigonometry from a higher and deeper perspective because of the introduction of complex numbers. People have been thinking about complex numbers for a long time, such as the root of the equation X2+ 1 = 0, but it was not until16th century that people seriously introduced imaginary number =i into mathematics. Then Euler established the famous Euler formula: ei θ = cos θ+. So a lot of problems in trigonometry can be easily solved. With the complex number and Euler formula, people can have a deeper understanding of the existing trigonometry theory, and some primitive and complicated methods and tools to deal with trigonometry can be "thrown aside".
In fact, trigonometry is an applied branch of mathematics. Although it originated from astronomy, it is very useful in many other disciplines.
One hundred years ago, Hilbert ended his famous speech with the following sentence: "The organic unity of mathematics is an inherent feature of this science, because it is the basis of all accurate natural science knowledge. In order to achieve this lofty goal smoothly, let the new century bring talented masters and countless enthusiastic believers to this science! " I am convinced that as long as we learn mathematics well and use it well from now on, the 2 1 century will certainly "bring talented masters to this science", and many of them must come from the post-90 s generation!
Note: simply put the online ones in order, which needs to be revised!