The Quantitative Geometric History Of The Development Of Secondary School Teaching

Abstract In the current junior high school mathematics textbooks,geometry is an important part of the culture students.Logical reasoning ability has an irreplaceable role.Geometry history of the development process is the first study of plane geometry,after study of three-dimensional geometry plane geometry first discuss the qualitative and quantitative analysis after China’s current junior high school mathematics textbooks based on Euclidean geometry as the main line.Ancient Greek Euclidean the quantitative plane geometry basis the quantitative plane geometry basis in ancient China different approach and demonstration. The formula for the area of Pythagorean formula-stings and access complementarity principle in ancient China comprehensive quantitative plane geometry basis.This article select the quantitative geometric formula for the area of and access complementarity principle as a starting point,the following issues:(1)Of ancient Greece Heron’s formula, Arab Times Khwarizmi a quadratic equation Root Formula area pieced together with access to the complementarity principle the recovery,and the formula for the area and the related access complementarity principle in the ancient Chinese mathematics were reviewed.(2)Select the Pythagorean theorem proved as the research object, the relationship of the area under the law and thinking in the analysis of cognitive point of view to discuss the area of law and access the complementarity principle intuitive features,compare Euclid interpretation and Oriental out-in complementary method differences.(3)Creation of problem situations,using the area method similar figures instructional design,and analysis of an area of law is not Can solve only the length of the line,the area of class,but also to solve the problem of inequality,triangle and probability,exhibition Shows the area method widely used in middle school mathematics teaching.The following conclusions by studying this article to enable students to acquire knowledge through the explanation of the history of mathematics.Generative principle to increase interest in mathematics penetration and out of the complementarity principle in teaching in a timely manners and area method can help students better understand the plane geometry.