a = 1.0
t = var('t')
xtreme=3
myaxes = line([[-xtreme,0],[xtreme,0]],rgbcolor = (0,0,0))
myaxes = myaxes + line([[0,-xtreme],[0,xtreme]],rgbcolor = (0,0,0))
def nephroid(theta):
    C = circle((0,0),a,rgbcolor = (0,0,0))
    A=[a,0]
    O=[0,0]
    M=[a*cos(theta),a*sin(theta)]
    l=a*sqrt(2*(1-cos(theta)))
    P1=[a*cos(theta)-l*a*cos(theta),a*sin(theta)-l*a*sin(theta)]
    P2=[a*cos(theta)+l*a*cos(theta),a*sin(theta)+l*a*sin(theta)]
    L1 = line([P1,P2])
    L2 = line([A,M])
    M=point(M)
    A=point(A)
    P1=point(P1)
    P2=point(P2)
    O=point(O)
    return C+O+A+M+P1+P2+L1+L2+myaxes


def Freeth(theta):
    ne = nephroid(theta)
    Freethplot = parametric_plot([(1+2*sin(t/2))*cos(t), (1+2*sin(t/2))*sin(t)],[t,0,theta], rgbcolor = (1,0,1))
    return ne+Freethplot

a2 = animate([Freeth(i) for i in srange(float(0),float(4*pi),float(pi)/30)],aspect_ratio=1)

a2.show()