【作者】 何援军；

【Author】 He Yuanjun (Dept.of Computer Science & Engineering,Shanghai Jiaotong University,Shanghai,200240,China)

【机构】 上海交通大学计算机科学与工程系；

【摘要】 几何与代数,作为数学的两个基本组成部分,原本分别考虑"形"和"数"的问题,理论上应该各占半壁江山,然而,历史并不是这样,两者并不平衡。在笛卡儿把代数中形式化符号体系的表示方法引进到几何学之后,走的基本上是"几何代数化"之路。这无意的削弱了几何的作用范围,掩盖了几何的自然属性,减弱了人类直觉这个最有力的武器。认为几何及几何计算是不应该全部被代数化的,在讨论"几何计算"的时候,需要在几何(含画法几何)、代数、物理、计算机方面找到一个平衡点——以"几何问题几何化"作为它的命题。引入"几何基"与"几何数",构筑了几何问题几何化的框架。更多还原

【Abstract】 As two major aspects of mathematics, geometry and algebra focus on shape and numeric respectively.Theoretically,they are comparable to each other.But,historically,they are not.After the introduction of formal symbol system from algebra into geometry by Descartes,geometry has been experiencing algebraization.Unfortunately,algebra -aization of geometry narrows down the scope of geometry,hides the natural characters of geometry and reduces the power of human intuition as weapon. This paper disagrees with simple algebraization. When discussing geometry computing,stable junctures should be found based on geometry (including descriptive geometry),algebra,physics and computer.As the topic of such discussion,"geometry problems should be solved geometrically".A framework of this topic is then built with "primary geometric functions" and "geometric numeric".更多还原