椭圆曲率中心轨迹——星形线的特性  

The Characteristic of the Astroid Which is the Track for the Curvature Center of a Ellipse

作　　者：邓小红 刘娅[2] 潘汉军[2] 

机构地区：[1]赣州市湖边中学,江西赣州341000 [2]湛江师范学院物理科学与技术学院,广东湛江524048

出　　处：《数学的实践与认识》2007年第17期179-186,共8页Mathematics in Practice and Theory

摘　　要：采用微分几何方法分析了椭圆星形线的多项特性,指出了其中星形线划分平面的特性对于椭圆上的点离已知点距离极值存在性的决定性作用,同时指出了星形线划分平面的特性对于确定椭圆上距离任意已知点最远或最近的点的位置具有决定性意义,提出了确定最远点及最近点的几何方法,阐明了最远点及最近点在各极值点之间的替换过程,为工程中确定圆柱面绕任意轴回转所形成的包络面的特性提供了依据.It analyses the characteristic of the astroid by the method of differential coefficient geometry, and points out the characteristic that astroid carve up plane decides being about the distance extremum and decides the location of the apoapsis and the proximate point, and puts forward a geometry method for fixing o＇ri the location of the apoapsis and the proximate point, and illustrates the replace process about the apoapsis or the proximate point among the extremum points. It provides a theory gist for the making certain of the characteristic of the envelope face which is formed during a column face rotates about a random known axis in engineering.

关 键 词：椭圆 星形线 微分几何 极值 

分 类 号：O186.1[理学—数学]