1314.sagews

from pylab import *

clf()
theta = arange(0,2*pi,0.001)
r = sin(theta)
polar(theta, r,'blue')
title('Circle')
savefig('Graf3.png')

clf()
theta = arange(0,4*pi,0.001)
r = theta
polar(theta, r,'blue')
title('Archimedean spiral: $r = \phi$')
savefig('Graf3.png')

clf()
theta = arange(0,2*pi,0.001)
r = exp(theta)
polar(theta, r,'blue')
title('logaritmic spiral: $r = e^{\phi}$')
savefig('Graf3.png')

clf()
theta = arange(0,2*pi,0.001)
r = sqrt(8*cos(2*theta))
polar(theta, r,'blue')
title('leminiscate $r = 8 \cos(2 \phi)$')
savefig('Graf3.png')

clf()
theta = arange(0,2*pi,0.001)
r = sqrt(8*cos(4*theta))
polar(theta, r,'blue')
title('leminiscate $r = 8 \sin(4 \phi)$')
savefig('Graf3.png')

clf()
theta = arange(0,2*pi,0.001)
r = 1+ cos(theta)
polar(theta, r,'blue')
title('limacon of Pascal $r = 1+ cos(\phi)$')
savefig('Graf3.png')

clf()
theta = arange(0,6*pi,0.001)
r = 3* sin(theta)/theta
polar(theta, r,'blue')
title('Cochleoid $r = 3 \sin(\phi)/ \phi$')
savefig('Graf3.png')

clf()
theta = arange(0,4*pi,0.001)
r = sqrt(10/theta)
polar(theta, r,'blue')
title('Cochleoid $r^2 = 10 / \phi$')
savefig('Graf3.png')

clf()
theta = arange(0,6*pi,0.001)
r = 1/ (3*theta+ 0.7*pi)
polar(theta, r,'blue')
title('Cotes spiral $r = 1/ (3\phi+ 0.7\pi)$')
savefig('Graf3.png')

clf()
theta = arange(0,6*pi,0.001)
r = sqrt(theta)
polar(theta, r,'blue')
title('Euler spiral $r =\phi^(1/2)$')
savefig('Graf3.png')