摘要
利用Gauss-Bonnet公式说明了几种常曲率空间中测地三角形的边角关系.证明了f(u)=cosu的几何凸性,并利用cosx～(1/2)的几何凸性证明了球面空间S2和双曲空间H2中测地三角形中的边角关系,与欧氏空间中E3的勾股定理相比,从形式和逻辑上都显示出完备性,彰显了分析与几何的内在和谐一致性.
By making use of Gauss-Bonnet Formula,the author in this paper not only explains the relationship between the sides and angles of geodesic triangles in several constant curvature spaces,but also proves it with the geometry convexity of cos√x. Compared with the Pythagorean theorem in Euclid space,It manifests completeness in both form and content. At the same time, it shows the internal harmony between analysis and geometry.
出处
《辽宁师范大学学报（自然科学版）》
CAS
北大核心
2008年第3期264-266,共3页
Journal of Liaoning Normal University:Natural Science Edition
基金
河南省自然科学基金资助项目(0511012700)
