Witch of Maria Agnesi

There's one on wikipedia like this, but for an upcoming class I wanted to do it in Sage:




xtreme = 4.1
myaxes = line([[-xtreme,0],[xtreme,0]],rgbcolor = (0,0,0))
myaxes = myaxes + line([[0,-1],[0,2.1]],rgbcolor = (0,0,0))
a = 1.0
t = var('t')
npi = RDF(pi)
def agnesi(theta):
mac = circle((0,a),a,rgbcolor = (0,0,0))
maL = line([[-xtreme,2*a],[xtreme,2*a]])
maL2 = line([[0,0],[2*a*cot(theta),2*a]])
p1 = [2*a*cot(theta),2*a*sin(theta)^2]
p2 = [2*a*cot(theta)-cot(theta)*(2*a-2*a*sin(theta)^2),2*a*sin(theta)^2]
maL3 = line([p2,p1,[2*a*cot(theta),2*a]], rgbcolor = (1,0,0))
map1 = point(p1)
map2 = point(p2)
am = line([[-.05,a],[.05,a]], rgbcolor = (0,0,0))
at = text('a',[-.1,a], rgbcolor = (0,0,0))
yt = text('y',[0,2.2], rgbcolor = (0,0,0))
xt = text('x',[xtreme + .1,-.1], rgbcolor = (0,0,0))
#tt = text('t',[.15,.1], rgbcolor = (0,0,0))
matext = at+yt+xt
ma = mac+myaxes+maL+am+matext+maL2+map1+maL3+map2
return ma

def witchy(theta):
ma = agnesi(theta)
agplot = parametric_plot([2*a*cot(t),2*a*sin(t)^2],[t,.001,theta], rgbcolor = (1,0,1))
return ma+agplot

a2 = animate([witchy(i) for i in srange(.1,npi-.1,npi/60)]+[witchy(i) for i in srange(npi-.1,.1,-npi/60)], xmin = -3, xmax = 3, ymin = 0, ymax = 2.3, figsize = [6,2.3], axes = False)

a2.show()