Wang Xiaotong on Right Triangles: Six Problems from ‘Continuation of Ancient Mathematics’ (Seventh Century AD)

Abstract

Wang Xiaotong’s 王孝通 Jigu suanjing 緝古算經 is primarily concerned with problems in solid and plane geometry leading to polynomial equa­tions which are to be solved numerically using a procedure similar to Horner’s Method. We translate and analyze here six problems in plane geometry. In each case the solution is derived using a dissection of a 3-dimensional object. We suggest an interpretation of one fragmentary comment which at first sight appears to refer to a dissection of a 4-dimensional object.