The Grand Astrologerʼs platform and ramp: Four problems in solid geometry from Wang Xiaotongʼs ‘Continuation of ancient mathematics’ (7th century AD)

Abstract

Wang Xiaotongʼs Jigu suanjing is primarily concerned with problems in solid and plane geometry leading to cubic equations which are to be solved numerically by the Chinese variant of Hornerʼs method. The problems in solid geometry give the volume of a solid and certain constraints on its dimensions, and the dimensions are required; we translate and analyze four of these. Three are solved using dissections, while one is solved using reasoning about calculations with very little recourse to geometrical considerations. The problems in Wang Xiaotongʼs text cannot be seen as practical problems in themselves, but they introduce mathematical methods which would have been useful to administrators in organizing labor forces for public works.