广义三角形—八卦—映射群

GENERALIZED TRIANGLE-EIGHT DIAGRAMS-MAPPING GROUP

本文运用变换群方法阐述了广义三角形的数学基础。广义三角形的实质系常规三角形经映射变换后的映象。从属于广义三角形变换群的广义三角形几何一共有九条定理。它在本质上不同于欧氏几何、仿射几何及射影几何。 广义三角形群与八卦群同构。以广义三角形原理为基础的机构电算法仅仅相应于六十四卦中的很小一部分。

In this paper, the fundamental mathmatics of generalized triangle is studied by the method of transformation group theory. The nature of generalized triaagle is a mapping image of the general triaagle. Generalized triangle geometry concerning generalized triangle transformation group has nine laws in all. It is different from Euclidean geometry, affine geometry and projective geometry etc. Generalized triangle group is isomorpic with the Eight Diagrams group. Mechanism computing method based on generalized triangle only corresponds with a little bit of Sixty-four Digrams. generalized triangle, mapping group, eight diagrams, Erlangen program, computing method of mechanism.