Setup

import math
import matplotlib
from matplotlib.animation import FuncAnimation as FA
from matplotlib.patches import Ellipse as mpE
from matplotlib.patches import Polygon as mpP
import matplotlib.pyplot as plt

def plotHelper(option) :
    
    fig = plt.figure(figsize = (12, 12))
    ax = fig.add_subplot(xlim = (-1.01, 1.01),
                         ylim = (-1.01, 1.01))

    #Remove axes and ticks.
    ax.spines["top"].set_visible(False)
    ax.spines["right"].set_visible(False)
    ax.spines["bottom"].set_visible(False)
    ax.spines["left"].set_visible(False)
    ax.set_xticks([])
    ax.set_yticks([])
    
    circ = mpE(xy = (0, 0),
               width = 2,
               height = 2,
               edgecolor = 'k',
               facecolor = '#440154FF')
    ax.add_patch(circ)
    sp = math.sqrt(3) / 2
    sn = -1 * sp
    
    if option == "Fiddler" :
           
        quads = mpP([(-1, 0), (-0.5, sp), (0.5, sp), (1,0),
                     (0.5, sn), (-0.5, sn), (-1, 0), (1, 0)],
                     edgecolor = 'k',
                     facecolor = '#2A788EFF')
            
        ax.add_patch(quads)
        
    elif option == "EC1" :
        
        quad = mpP([(0, 1), (1, 0), (0, -1), (0, 1)],
                   edgecolor = 'k',
                   facecolor = '#2A788EFF')
        
        tri = mpP([(-1, 0), (0, 1), (0, -1), (-1, 0)],
                  edgecolor = 'k',
                  facecolor = '#7AD151FF') 
        
        ax.add_patch(quad)
        ax.add_patch(tri)
        
    else :
        
        quad = mpP([(0.5, sp), (1, 0), (0.5, sn), (0.5, sp)],
                   edgecolor = 'k',
                   facecolor = '#2A788EFF')
        
        tri = mpP([(-1, 0), (0.5, sp), (0.5, sn), (-1, 0)],
                  edgecolor = 'k',
                  facecolor = '#7AD151FF')
        
        ax.add_patch(quad)
        ax.add_patch(tri)    
        
        if option == "EC3" :
            
            length = mpP([(-1, 0), (1, 0)],
                          edgecolor = 'k')
            
            rad = mpP([(0, 0), (0.5, sp)],
                      edgecolor = 'k', ls = ':')
        
            root = mpP([(0.54, 0.335), (0.7, 0.335)],
                       edgecolor = 'k', lw = 0.85)
        
            ax.add_patch(length)
            ax.add_patch(rad)
            ax.add_patch(root)
        
            text = [("r", (-0.5, -0.05)),
                    ("r", (0.25, 0.3)),
                    ("a", (0.25, -0.05)),
                    ("√r²-a²", (0.6, 0.3)),
                    ("r-a", (0.75, -0.05))]
        
            for t in text :
                plt.annotate(t[0], t[1], c = "k", fontsize = 24,
                             ha = "center", va = "center")
            
    fig.savefig("2023.11.10" + option + ".png", bbox_inches='tight')

plotHelper("Fiddler")

plotHelper("EC1")

plotHelper("EC2")

plotHelper("EC3")

matplotlib.rc_file_defaults()

fig = plt.figure(figsize = (10.5, 7))
ax = fig.add_subplot(xlim = (-1.01, 2.02),
                     ylim = (-1.01, 1.01))

ax.set_title("Maximizing the Quadrilateral + Triangle Areas", fontsize = 24)

#Remove axes and ticks.
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["bottom"].set_visible(False)
ax.spines["left"].set_visible(False)
ax.set_xticks([])
ax.set_yticks([])

font = {'size' : 20}

#Eight artists:
#Circle, Quadrilateral, Triangle, Length.
#Length Text, Quadrilateral Area, Triangle Area, Total Area

circ = mpE(xy = (0, 0),
           width = 2,
           height = 2,
           edgecolor = 'k',
           facecolor = '#440154FF')

quad = mpP([(-1, 0)],
           edgecolor = 'k',
           facecolor = '#2A788EFF')
        
tri = mpP([(-1, 0)],
          edgecolor = 'k',
          facecolor = '#7AD151FF')

leng = mpP([(-1, 0)],
           edgecolor = 'k')

length_text = ax.text(-0.95, 0, '', ha = 'left', **font)
quad_text = ax.text(1.03, 0.3, '', **font, color = '#2A788EFF')
tri_text = ax.text(1.03, 0, '', **font, color = '#7AD151FF')
tot_text = ax.text(1.03, -0.3, '', **font)


def init():
    """Initialize seven artists."""
    ax.add_patch(circ)
    ax.add_patch(quad)
    ax.add_patch(tri)
    ax.add_patch(leng)

    length_text.set_text('')
    quad_text.set_text('')
    tri_text.set_text('')
    tot_text.set_text('')
    
    return circ, quad, tri, leng, length_text, quad_text, tri_text, tot_text

def animate(i):
    
    a = i/1000
    x = i/1000 - 1
    yp = math.sqrt(1- x**2)
    yn = -1 * yp
    quad_a = 2*yp / math.pi
    tri_a = a*yp / math.pi
    tot_a = (2+a)*yp / math.pi
    
    """Update eight artists."""
    
    quad.set_xy([(-1, 0), (x, yp), (1, 0), (x, yn), (-1, 0)])
    tri.set_xy([(-1, 0), (x, yp), (x, yn), (-1, 0)])
    leng.set_xy([(-1, 0), (x, 0)])
  
    length_text.set_text("%.4fr" % a)
    quad_text.set_text("Quad: %.4f%% of Circle" % quad_a)
    tri_text.set_text("Triangle: %.4f%% of Circle" % tri_a)
    tot_text.set_text("Total: %.4f%% of Circle" % tot_a)

    if i > 413 :
        length_text.set_x(x)
        length_text.set_ha("right")
    
    return circ, quad, tri, leng, length_text, quad_text, tri_text, tot_text

#Run animation.
anim = FA(fig, animate, init_func = init, frames = 2000, interval = 5, blit = True)       

#Save animation.
anim.save('2023.11.10 EC.mp4');

Rohan Lewis

2023.11.10