Vol.3 No.6 (November 2013)

# 初等几何的实践性基础及其应用———几何学的产生Practicalities Foundations of Elementary Geometry and Its Applications———The Produce of Geometry

There is a gap between the current geometry theory and its practice applications. The point, straight line, ray, parallel line and plane in current geometry possess the character of ideal all. They are the limit of se- quence of approximation point, straight line, ray, parallel line and plane separately, when the error bounds tend to zero. But the limit possesses the characteristic that could not be arrived at. Therefore, the character of only existence and ideal congruence of ideal point, straight line, ray, parallel line and plane must apply axi- oms to affirm them. In researching three-dimensional actual space, for ideal geometry element, the system of Euclidean geometry is suitable and necessary; but it needs a process of “negation of the negation” to apply it in reality question. Two questions of consistency of the axiom system and practice function of axioms could not be settled by the method of formal logic and the method of mathematical logic. The settlement of the two questions must apply the method of materialist dialectics.

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