论文标题
毕达哥拉斯在表面上的概括
A generalization of Pythagoras on a surface
论文作者
论文摘要
我们分析了托普诺戈夫的正弦定理，以在c^2常规表面M上使用无限的地理三角形ABC，这在他的书中给出了[6，问题3.7.2]，我们在M. c = \fracπ{2 pers of per n of per of per n of per n of in of py n of py n of Aciags obc on abc上的概括性提供了综合的概括。 = ab^2 + bc^2 + f（\角a，\fracπ{2}，ab，bc）o（ac^2）或ac^2 = ab^2 + bc^2 +（\ angle a + \ angle a + \ angle c- \fracπ{2}）其中f（\ anger a，b，b，ab bc bc）是a r rations a r rations a r rations a r rations w n f（\ angle a，begne去科萨； Cosb，Sina，Sinb，AB和BC。
We analyze Toponogov's sine theorem for an infinitesimal geodesic triangle ABC on a C^2 regular surface M, which is given in his book [6, Problem 3.7.2] and we provide a generalization of the law of cosines for ABC on M. By replacing in the law of cosines B=\fracπ{2} on M, we derive the generalized theorem of Pythagoras on a surface: AC^2 = AB^2 + BC^2 + f(\angle A,\fracπ{2},AB,BC)o(AC^2) or AC^2 = AB^2 + BC^2 + (\angle A + \angle C-\fracπ{2})^2 where f(\angle A,\angle B,AB,BC) is a rational function w.r. to cosA; cosB, sinA, sinB, AB and BC.
