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The Effects on Spatial Visualization after the Introduction of Vector into Solid Geometry

Author: ZhangLiuJun
Tutor: XiongBin
School: East China Normal University
Course: Education
Keywords: geometric method vector method
CLC: G634.6
Type: Master's thesis
Year: 2009
Downloads: 223
Quote: 0
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Abstract


Euclid(Euclid,about 275 BC--330 BC) wrote the "Elements" around 300 BC,a total of 15 volumes,of which 11-13 volumes were about solid geometry.Since the vector theory has not yet created,from the "Elements" introducing the vector method to the solid geometry,which is approximately three thousand years,the primary purpose of people learning solid geometry is training spatial thinking.Space imagination is trained in solving problems in solid geometry training.That is to say,training space imagination of geometry shape,size,site and understanding and processing capacity of sports change.In the study of the solid geometry,on the one hand,attention should be paid to the differences between three-dimensional graphics problems and the plane figure. Consideration the question should be focused on the whole space not confined to a plane. On the other hand,the three-dimensional graphics must pay attention to the difference with the plane figure.Vector is just a tool.After the introduction of vector into solid geometry,spatial thinking of many problems is down.But at the same time,relatively speaking,calculation is increasing.The purpose of students learning solid geometry is to develop space thinking ability.After the introduction of vector,whether or not the impact of spatial thinking to students and how deep the impact will be the focus of this paper.With the introduction of vector space,many of the problems no longer need planarization of three-dimensional plane,but directly use vector methods,such as solving a straight line and a plane as the angle,the plane angle of dihedral angle,etc.The method used is to strengthen the mastery of the vector which based on solid geometry.On the contrary,in the study of solid geometry,we should base on vector as a carrier to enhance the cultivation of spatial thinking.

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