Some Examples of the Use of Distances as Coordinates for Euclidean Geometry
Some Examples of the Use of Distances as Coordinates for Euclidean Geometry
复制标题
使用距离作为欧几里得几何坐标的一些例子
DOI：
10.1016/s0747-7171(08)80120-4
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Timothy F. Havel
中科院分区：
文献类型：
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作者：
Timothy F. Havel
距离几何为我们提供了一个隐含的特征欧几里德度量的一个系统的多项式方程和不等式。借助计算机代数程序，这些方程和不等式反过来又为我们提供了一种无坐标的方法来证明欧几里得几何中的定理。本文简要总结了这种方法所依据的数学结果，并举例说明了它是如何应用的。特别是，我们展示了如何可以用来推导出一个简单的连杆机构的拓扑结构。
Distance geometry provides us with an implicit characterization of the Euclidean metric in terms of a system of polynomial equations and inequalities. With the aid of computer algebra programs, these equations and inequalities in turn provide us with a coordinate-free approach to proving theorems in Euclidean geometry analytically. This paper contains a brief summary of the mathematical results on which this approach is based, together with some examples showing how it is applied. In particular, we show how it can be used to derive the topological structure of a simple linkage mechanism.