摘要
提出了布尔梅斯特 (Burmester)曲线的一种新的形成方法 .即成射影对应的直线束和二次线束的对应直线垂直相交 ,则其垂足轨迹生成布尔梅斯特曲线 :(x2 +y2 ) (lx+my) -mlxy=0 .对其进行了解析证明 ,并提出了它的作图方法 .通过求二次线束的包络 ,又得出一个重要的结论 :自抛物线准线上一点向抛物线的切线作垂线 ,其垂足曲线为布尔梅斯特曲线 .
There is a new formation of the curvilinearity of the Burmester:When the perpendicularity of a quadratic ray intersects the projection of the homologous beeline ray, the track of the perpendicular point creates Burmester curvilinearity:(x 2+y 2)(lx+my)-mlxy=0. After it was parsed, the method of using it in drawing was brought forward. Through the process of calculating the envelope curve of the quadratic ray, another important ultimateness was made: the perpendicular line from a point of a parabola's directrix to the tangent of a parabola, the curvilinearity of the perpendicular point is Burmester curvilinearity,which gives a theoretical and mathematical evidence to the computer research and making Burmester curvilinearity.
出处
《湘潭大学自然科学学报》
CAS
CSCD
2002年第4期70-72,共3页
Natural Science Journal of Xiangtan University
