黔东南山区水车水碾数学元素调查分析

Investigation and Analysis on mathematical elements of water wheel mill in Southeast Guizhou mountainous area

运用实地调查法、数理分析法,对黔东南水车水碾取水竹筒运动轨迹与安装位置间的关系、水轮车与碾石角速度间的关系、碾石上某点的运动轨迹与轴旋转圆心角间的关系所蕴含的数学元素进行研究,研究发现,水车水碾存在丰富的代数与几何知识,主要体现为初等几何、三角函数、曲面与方程、“二分法”以及“最优化”的思想方法。

Based on the field investigation and mathematical analysis,this paper studies the relation⁃ship between the track of bamboo barrel and the installation position,the angular velocity of the wheel and the rolling stone,and the mathematical elements contained in the relationship between the track of a point on the rolling stone and the rotation circle angle of the axis.It is found that there are abundant algebraic and geometric knowledge in water mill,which are mainly embodied in elementary geometry,trigonometric function,surface and equation,dichotomy and optimization.