The presentation of a spiral-drawing program culminates in this program.

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from turtle import * 
from math import * 
pensize(10) 
pencolor("blue") 
penup() 
radius = 20 
goto(radius,0) 
pendown() 
for i in range(1,300): 
  newangle = 2*i*pi/100 
  goto( radius*cos(newangle), 
        radius*sin(newangle) ) 
  radius = radius + 1

Two significant changes from the earlier circle-drawing program are seen above.
First, radius is redefined to be one unit larger, each time variable i steps through its sequence of numbers. Second, the sequence of numbers is not 1-100, but instead 1-299, even though the angle variable newangle calculation is in terms of 1/100th of a full sweep around the circle. In effect, the larger sequence 1-299 amounts to going about three times around the circle. Drawing three times around a circle would not be needed to draw a circle, but because the radius is increasing, the program draws a spiral.

Two interesting pointers related to this example are: