#来自在线整数序列百科全书的问候!http://oeis.org/搜索:id:a332528显示第1-1页,共1页%一A332528%S A332528 1,1,1,5,3,9,8,6,1,6,3,6,7,0,8,4,7,8,8,5,2,3,6,7,2,0,2,2,8,1,3,2,6,6,%T A332528 5,7,6,5,4,7,5,1,2,0,8,1,8,4,5,3,1,7,7,7,4,4,4,4,1,0,3,3,5,8,5,6,%U A332528 3,4,6,7,6,8,6,4,7,3,9,2,1,7,4,3,2,3%A328正割函数的最大曲率展开式。%cA332528 y=secx图的最大曲率出现在每个分支上的两点(x,y)。其中一个点的y>0。设T为通过(0,1)且位于第一象限的分支。最大曲率K出现在一个点(u,v):%C A332528 u=0.4699525116436647246673202362884385302603014858623133147。。。%C A332528 v=1.121592022152314185447100088419469957967272605862403985。。。%C A332528 K=1.1153986163670878852367202281326657654751208184531773740。。。%C A332528(u,v)处的密切圆有%C A332528中心=(x,y)=(0.02618081309772817465,,,,1.900598757881329358432040976889617…)。%C A332528半径=1/K=0.896540470219566446984489512566284091376257661443。。。%C A332528最大曲率:K=1.1153986163670878852367202281326657654751208184531773740。。。%t A332528 maxC=ArcCos[Sqrt[(2*(2-Sqrt[31]*Cos[(Pi+ArcTan[(9*Sqrt[302])/73])/3])/3]];%t A332528 centerMaxC={(-3*x+x*Cos[2*x]+Sin[2*x]+2*Tan[x]^3)/(-3+%t A332528 Cos[2*x]),-((Cos[x]*Cos[2*x])/(-3+Cos[2*x])+(3*秒[x])/%电话:A332528 2}/。x->最大值;%t A332528 rMin=(Sqrt[(7+Cos[4 x])^3]秒[x]^3)/(Sqrt[2]8(3-Cos[2 x]))/。x->最大值;%t A332528显示[绘图[秒[x],{x,0-3/2,2}],%t A332528图形[{PointSize[Large],红色,Point[centerMaxC],%t A332528点[{maxC,Sec[maxC]}],圆[centerMaxC,rMin],%t A332528行[{centerMaxC,{maxC,Sec[maxC]}}]}],AspectRatio->Automatic,%t A332528绘图范围->{0,2}]%t A332528 x=弧角[Sqrt[(2*(2-Sqrt[31]*Cos[(Pi+ArcTan[(9*Sqrt[302])/73])/3]))/%电话:A332528 3]];(*最大曲率出现在(x,sec x)*)%t A332528{N[x,150],N[秒[x],150]}%t A332528{cx,cy}={(-3*x+x*Cos[2*x]+Sin[2*x]+2*Tan[x]^3)/(-3+Cos[2*x]),-((Cos[x]*Cos[2*x])/(-3+Cos[2*x])+(3*Sec[x])/2};(*密切圈中心*)%电话:A332528{N[cx,150],N[cy,150]}%t A332528 r=N[Sqrt[(x-cx)^2+(Sec[x]-cy)^2],150](*曲率半径*)%t A332528 1/r(*曲率*)%t A332528 kr=实数[1/r][[1]]%t A332528(*彼得J.C.摩西,2020年5月7日*)%Y A332528,参见A332527。%K A332528无,cons%O A332528 0,4%A332528克拉克金伯利,2020年6月21日#根据OEIS最终用户许可协议提供内容:http://oeis.org/LICENSE