【摘要】 曲线C在点P(x0,y0)曲率圆是与该曲线C相切于点P(x0,y0)(凹侧)的最大圆,曲率圆的圆心D的轨迹曲线G称为曲线C的渐屈线。抛物线y2=2px(p>0)、椭圆x2/a2+y2/b2=1和双曲线x2/a2-y2/b2=1的渐屈线方程分别为y2=8/(27P)(x-p)3、(2/X3)/(c2/a)2/3+(2/y3)/(c2/b)2/3=1和(2/X3)/(c2/a)2/3-(2/y3)/(c2/b)2/3=1.抛物线、椭圆和双曲线的最小曲率圆都是它们的内切圆,其方程分别为(x-p)2+y2=p2、〔x±c2/a〕2+y2=b4/a2、〔x±c2/a〕2+y2=b4/a2。更多还原

【Abstract】 Curve C at the spot P(x0,y0) curvature is the maximal circle(concave side) of the curve C tangency at the spot P(x0,y0). Contrail curve G of the center D of curvature circle entitles evolute of curve C. The evolute equations of parabola y2=2px(p>0),ellipse x2/a2+y2/b2=1 and hyperbola x2/a2-y2/b2=1 are respectively as follows: y2=8/(27P)(x-p)3、(2/X3)/(c2/a)2/3+(2/y3)/(c2/b)2/3=1and(2/X3)/(c2/a)2/3-(2/y3)/(c2/b)2/3=1.. The minimum curvature circles of parabola,ellipse and hyperbola all are their inscribed circle,their equations are(x-p)2+y2=p2、〔x±c2/a〕2+y2=b4/a2 and〔x±c2/a〕2-y2=b4/a2 respectively.更多还原