## Thursday, July 23, 2009

### Witch of Maria Agnesi

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

xtreme = 4.1myaxes = line([[-xtreme,0],[xtreme,0]],rgbcolor = (0,0,0))myaxes = myaxes + line([[0,-1],[0,2.1]],rgbcolor = (0,0,0))a = 1.0t = 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 madef 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+agplota2 = 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()

mvngu said...

Can you put this animation up somewhere on the Sage wiki?

M. Hampton said...

OK, I put it on http://wiki.sagemath.org/pics.

-Marshall

Pamela said...

Is she flying on her broom?