婆什伽罗关于球表面积公式的计算方法复原

Restoring Bhaskara's Formula of the Area of the Sphere

婆什伽罗利用他所熟知的印度三角函数知识,给出了球表面积公式的两种证明方法,即月牙形方法和环带形方法.根据印度当时的数学发展,婆什伽罗其实是沿着经纬线的方向将球分割为24等份,并求出了球的表面积公式.据此对提出古代印度使用无限分割方法的观点进行了商榷,也由此得出婆什伽罗仅仅具备了朴素的极限思想方法的萌芽.

With the knowledge of Hindu trigonometric functions,two reconstructive methods,crescent and zone figure,were given by Bhaskara to prove the area formula of the sphere.In fact Bhaskara s method divided sphere into 24 quarters.It then can be concluded that Bhaskara only held the ideas of sprout of limit.As a result,the views of infinitum segmentation on sphere are deliberated.