Graphics-Array.ipynb

Kernel: SageMath 9.2

See the family of figures at the end of section 10.3

We show how to make a figure containing several curves, but not on the same axis systems.

We plot several members of the family of curves $$r = 1+c\sin \theta$$ and we arrange the curves in an array.

var('t')
C=[2.5, 1.7, 1, 0.7, 0.5, 0.2, 0, -0.2, -0.5, -0.8, -1, -2] # The list containing the values for c
Curves = [polar_plot(1+c*sin(t),0,t,2*pi) for c in C]
Array = graphics_array(((Curves[0],Curves[1], Curves[2], Curves[3]),
                     (Curves[4],Curves[5], Curves[6], Curves[7]),
                     (Curves[8],Curves[9], Curves[10], Curves[11])))
                     
Array.show(figsize  = 8)                     

Thge result is pretty good, but some improvements can be done:

• For instance one may want to put a legend telling what is the value of $c$ corresponding to each figure,

• The font size of the axes are slightly big.

The two improvements are obtained by running a loop through all the elements in the list Curves. See what is the effect of changing the loc value

var('t')
C=[2.5, 1.7, 1, 0.7, 0.5, 0.2, 0, -0.2, -0.5, -0.8, -1, -2] # The values for c
Curves = [polar_plot(1+c*sin(t),0,t,2*pi, legend_label = '%s'%c.n(digits=2)) for c in C]

for g in Curves:
    g.set_legend_options(font_size = 8, loc = 7)
    g.fontsize(8)
    
    
Array = graphics_array(((Curves[0],Curves[2], Curves[2], Curves[3]),
                     (Curves[4],Curves[5], Curves[6], Curves[7]),
                     (Curves[8],Curves[9], Curves[10], Curves[11])))
Array.show(figsize  = 9)