婆什伽罗球表面积公式的古证复原

Revisiting Bhaskara's Formula of the Sphere's Surface Area

根据婆什伽罗的数学思想,并利用他熟知的三角函数和射影知识, 给出了其球表面积公式的两种证明方法,即月牙形方法并口环带形方法。由此得出,婆什伽罗不仅已经具备了初步的极限观念,而且还在曲面求积方面做出了重要贡献,从而对一些学者关于婆什伽罗的某些观点提出了商榷。

With the knowledge of trigonometric functions and projection known by Bhaskara, two reconstructive proofs of Bhaskara＇s formula of the surface area of a sphere, the methods of crescent and zone, are given by the principles of reconstructing ancient proofs. It can thus be concluded that Bhaskara not only held primitive ideas of limit, but also had gained significant achievements in the field of calculus of curved surface. As a result, some traditional views on Bhaskara are deliberated.