# Author: Ika, 2013-09-15  import numpy as np import matplotlib.pyplot as plt import scipy.special as sp from matplotlib.patches import Polygon import random                                                                          fig=plt.figure() ax = fig.add_subplot(111)  ax.set_xlim(0,2) ax.set_ylim(0,4)  X = np.arange(0,2.01,0.01) Y = X*X # Plot the curve and area. ax.plot(X, Y)  verts = [(0,0)] + zip(X,Y) + [(2,0)] poly = Polygon(verts, facecolor='blue',alpha=0.5,edgecolor='blue') ax.add_patch(poly) plt.savefig("frame0100.jpg")  # Generate the files for the sums. ord = 0; while (ord<7): 	plt.clf() 	fig=plt.figure() 	ax = fig.add_subplot(111) 	interval = 1.0/(2**ord) 	ax.set_xlim(0,2) 	ax.set_ylim(0,4)  	X = np.arange(0,2.01,0.01) 	Y = X*X  	ax.plot(X, Y) 	ax.text(0.2,3.0,'Step=1/'+str(2**ord),size=36); 	x=interval; 	while (x<2+interval/2.0): 		verts = [(x-interval,0)]+[(x-interval,x*x)]+[(x,x*x)]+[(x,0)]; 		poly = Polygon(verts, facecolor='blue', alpha=0.5,edgecolor='black') 		ax.add_patch(poly) 		x=x+interval;  	plt.savefig("frame00"+str(ord)+".jpg"); 	 	ord = ord+1;