Brief introduction to the history of geometry

The development of geometry has roughly gone through four basic stages.

The Formation and Development of Experimental Geometry

Geometry originated from the observation of the shape and arrangement of stars in the sky, and from the needs of practical activities such as measuring land, measuring volume, making utensils and drawing graphics. On the basis of observation, practice and experiment, people have accumulated rich geometric experience, formed many rough concepts, reflected the relationship between some empirical facts, and formed experimental geometry. Geometry studied in ancient China, ancient Egypt, ancient India and Babylon is basically the content of experimental geometry.

For example, Pythagorean theorem, simple measurement knowledge, was discovered very early in ancient China. There are "one (circle), its first equal length" and "flat (parallel), its first equal height" in Mojing. Ancient Indians believed that "the area of a circle is equal to the area of a rectangle, the bottom of the rectangle is equal to half a circle, and the height of the rectangle is higher than the radius of the circle".

2. The formation and development of theoretical geometry.

With the trade and cultural exchange between ancient Egypt and Greece, Egyptian geometry knowledge was gradually introduced into ancient Greece. Many mathematicians in ancient Greece, such as Thales, Pythagoras, Plato and Euclid, made great contributions to the study of geometry. In particular, Plato introduced the thinking method of logic into geometry. Establish detailed definitions and clear axioms as the basis of geometry, and then Euclid compiled thirteen volumes of Elements of Geometry on the basis of predecessors' geometric knowledge and in accordance with a strict logical system, laying the foundation for theoretical geometry (also known as deductive geometry, axiomatic geometry, Euclid geometry, etc.). ) and become a prestigious masterpiece in history.

Although the Elements of Geometry has some defects, such as incomplete axioms and sometimes resorting to intuition. , is a masterpiece of ancient mathematics, with rigorous argumentation and far-reaching influence. The axiomatic method used points out the direction for the future development of mathematics, and even becomes a milestone in the history of human civilization and a treasure in the cultural heritage of all mankind.

3. The emergence and development of analytic geometry.

In the 3rd century A.D., the appearance of Geometry Elements laid the foundation of theoretical geometry. At the same time, people have also done some research on conic curves and found many properties of conic curves. But in the later period, theology occupied a dominant position in feudal society, and science did not get the attention it deserved. It was not until 15 and 16 centuries that European capitalism began to develop and natural science developed rapidly with the actual needs of production. French Descartes found in his research that Euclidean geometry relies too much on graphics, while traditional algebra is completely subject to formulas and laws. They think that the traditional method of studying conic curves only pays attention to geometry and ignores algebra, and strongly advocate combining geometry and algebra to learn from each other's strengths, which is a new way to promote the development of mathematics.

4. The emergence and development of modern geometry.

In the process of the development of elementary geometry and analytic geometry, people constantly find that the elements of geometry are not strict in logic, and constantly enrich some axioms, especially the failure of trying to prove that the fifth postulate "A straight line intersects with the other two straight lines, and when the sum of the internal angles on the same side is less than two right angles, the two straight lines intersect on this side" has prompted people to re-examine the logical basis of geometry and made outstanding research results in two aspects.