#halvingSquares.py
#each smaller square is half the area of the previous

from ezgraphics import GraphicsWindow
import math

sqr = int(input("Enter square size of graphics window: "))

win = GraphicsWindow(sqr,sqr)
canvas = win.canvas()

x = y = 0
width = sqr
# SQR*(1/root2)**x > 4 pixels width...  solve:
# x > ln4/ln(1/root2) - lnSQR/ln(1/root2)
# x > -4 - lnSQR/-.34657
max_loops = -4 - math.log(sqr)/-.34567

for i in range(1,int(max_loops)+2):
    x += (width*(1-1/math.sqrt(2))) / 2
    y += (width*(1-1/math.sqrt(2))) / 2
    print("width:",int(width),"area:",int(width*width),int(x),int(y))
    width = (1/math.sqrt(2))**i * sqr
    canvas.drawRectangle(x,y, width,width)
    

print("Look at the graphics window")