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CosCircle_Evolute
2 seconds ago by admin
var('t') r=10; k=10; a(t)= ((r+cos(k*t))*cos(t), (r+cos(k*t))*sin(t)) parametric_plot( a(t), (t, 0, 2*pi), color='red')
a1=derivative(a,t) a2=derivative(a1,t)
k=((a1[0]*a2[1] - a2[0]*a1[1])/((a1.norm())^3)) T=a1/(a1.norm()) T1=derivative(T,t) KV=(T1/(a1.norm())) beta=a+( KV/(k^2))
plot(1/(k*k) , (t, -pi/20, pi/20))
var('s') rad(s,t)=(cos(s)/k, sin(s)/k) c=beta+rad
plotCurve = parametric_plot( a(t), (t, -pi/20, pi/20),thickness=3,color='red'); plotEvolute = parametric_plot( beta(t), (t,-pi/20, pi/20), color='grey'); plot([plotCurve, plotEvolute],aspect_ratio=1)
plotCircles = [parametric_plot( c(s,t), (s, 0, 2*pi) ,rgbcolor=(1-2*t/pi,1,2*t/pi))for t in [-pi/20 .. pi/20,step=pi/100]] ; plot([plotCircles, plotCurve, plotEvolute],aspect_ratio=1)