A Chinese mathematical classic of the third century: The sea island mathematical manual of Liu Hui

AbstractThe Haidao suanjing [Sea island mathematical manual], written by the Chinese mathematician Liu Hui in 263 a.d., consists of nine surveying problems whose solution schemes involve the use of right triangle theory and result in a variety of techniques and formulas for determining distances to inaccessible points. Liu's results were obtained through the use of a prototrigonometry based on the concept of chong cha. This paper presents a translation of the Haidao's mathematical exercises and solution formulas and considers some of the implications of this early mathematical work