论文标题
标准化的坐标几何形状应用于四面体的仿射有理三角学
Standardised co-ordinate geometry applied to affine rational trigonometry of a tetrahedron
论文作者
论文摘要
通过标准的四面体定义了三维仿射空间中标准化坐标的想法。通过对一般四面体上进行仿射图，我们可以用特定的四面体在一般的度量结构上的研究代替特定的四面体结构上的一般四面体的研究。使用Wildberger的理性三角学的框架以及作者先前工作中广义标量和矢量产物的定义，我们将计算与标准四面体相关的各种三角不变的不变剂，目的是证明没有这种机械机制难以证明的更为复杂的结果。
The idea of standardised co-ordinates in three-dimensional affine space is defined, by way of the Standard tetrahedron. By performing an affine map on a general tetrahedron, we may replace the study of a general tetrahedron over a specific metrical structure with the study of a specific tetrahedron over a general metrical structure. Using the framework of Wildberger's rational trigonometry as well as the definitions of generalised scalar and vector products in the author's previous work, we will compute the various trigonometric invariants associated to the Standard tetrahedron, with the purpose of proving some more complicated results which are difficult to prove without this mechanism.
