< Back

Lab 12: Scope and Functions

As usual, create a directory to hold today's files. All programs that you write today should be stored in this directory. 

$ cd ~/cs120/labs
$ mkdir lab12 
$ cd lab12

Practice 1

Write a function called equilateral_area(edge_length) that computes the area of an equilateral triangle with the specified edge length.

\[area = \frac{\sqrt{3}}{4} \times length ^ 2 \] 








  
Practice 2




  Copy and paste your solution to the previous exercise into this one,
  and use it when writing a function
  called sierpinski_area(edge_length) that computes the
  area of a Sierpinski triangle of order one.  A Sierpinski Triangle of
  order one is an equilateral triangle with a triangular hole.  The
  vertices of the hole triangle are the mid points of the Sierpinski
  triangle's edges.  For example:




  




  


  

  

    
  

  








Trees



  When working with functions, abstraction is key.  You will soon find
  yourself in a position where you start thinking about problems in
  functions.  Being able to break a complex problem, like an advanced
  drawing, into smaller and simpler problems which can be solved with
  a function can make your code a lot easier to write, and a lot
  easier to read.



Details



  Create a function draw_tree(pen, x_location, y_location,
  width) in a file called forest.py. This function
  should take as a parameter a turtle object (pen) which can
  be used to draw a tree to the turtle window.  The base of the tree
  should be centered around the point \((x\_location, y\_location)\) and
  the largest set of branches should have a width as
  specified.  Your tree should look like the tree in the picture in
  the example below.




  Notice that a tree is defined by a brown square, and four green
  triangles which overlap each other.  For this, define two additional
  functions in the same file.  The first should be called
  draw_square(pen, x_location, y_location, side_length)
  which draws a filled in brown square square centered around the
  specified point.  The second should be
  called
  draw_triangle(pen, x_location, y_location, side_length),
  which creates an equilateral triangle with the specified side length
  centered around the specified point.




  It should also be noted that each triangle is \(10\%\) smaller than
  the triangle below.




  Test your function by calling the function multiple times with
  different parameters.  Make sure your code follows the course's code
  conventions.



Example Output

Turtle Drawing of a Tree




Hint



  
  

    
    
      
      
      
      
      
      
      
      

      
  • 
	You have already written code that draws an equilateral
	triangle in a post lab.  Look back at that code for help
	writing the draw_triangle function.
      
    • 

      
  • 
	Your draw_tree function should consist basically
	of one call to draw_square and four calls
	to draw_triangle.  You can use a for loop to make
	drawing the four triangles easier.
      
    • 

      
  • 
	You can use variable reassignment to keep track of
	the width of the next triangle to be drawn.  If at loop
	iteration 0 your width was 100, you want the width of the
	next triangle to be 90 at loop iteration 1.  You can compute
	this by multiplying 
	the current width by .9, and assigning the value back into
	your variable storing current width.
      
    • 
    

  






  
Challenge

  

    Using a for loop, draw a full forest of trees.  You should use a
    for loop to draw the following collection of trees.
  

Turtle Drawing of a Forest







Twin Paradox



  In the year 2047, a set of twins were born.  One of these twins was
  placed in a rocket and launched towards a distant star at a
  significant percentage of the speed of light.  Unlike Superman,
  however, the rocket was programmed to return home after reaching
  its destination.  Because of the laws of relativity, the twin who
  was launched into space at close to the speed of light will have
  aged significantly less than their sibling.  The real question is,
  how much younger are they?



Details



  Create the function
  compute_age_difference(distance_traveled, percentage_of_light)
  in a file called twin_paradox.py.
  This function should take as parameters an integer representing a
  distance traveled in meters, and a floating point value in the range
  \((0, 1)\) which represents how close to the speed of light the twin
  traveled.  Your function should use the laws of relativity to
  compute how many years younger the twin is.




  Note that we are assuming all acceleration is instant, so we can
  simplify the equations.  The speed of light is
  \(2.99 \times 10 ^ 7 \mbox{ } \frac{m}{s^2}\),
  and the number of seconds passed on earth
  can be computed using time equation below, and the percentage of time
  passed on the rocket as compared to earch can be computed using
  dialation equation below.
  $$
  \begin{eqnarray}
  time &=& 2 \times \frac{distance}{speed\_traveled}\\
  \\
  dialation &=& \sqrt{1 - \frac{speed\_traveled}{speed\_of\_light ^ 2}}
  \end{eqnarray}
  $$




  Test your function by calling the function multiple times with
  different parameters.  Make sure your code follows the course's code
  conventions.



Test Cases





  
    

      Parameters
      Expected Output
    

  
  
    

      4 light years, 90% speed of light
      5.071622487746852
    

    

      4 light years, 50% speed of light
      2.1680934673491077
    

    

      0 light years, 90% speed of light
      0.0
    

    

      1 light year, 90% speed of light
      1.267905621936713
    

    

      1 light year, 50% speed of light
      0.5420233668372769
    

    

      10 light years, 99% speed of light
      17.550499006858566
    

    

      10 light years, 99.999% speed of light
      20.138324055460178
    

  





Hint



  
  

    
    
      
  • 
	Write a function
	called
	convert_light_years_to_meters(light_years),
	which converts a distance in light years to meters.  One light year
	is \(9.56 \times 10 ^ {15}\) meters.
      
    • 

      
  • 
	The time equation listed above returns the time that has passed on
	Earth in seconds.  Write a function called
	convert_seconds_to_years(seconds), which returns
	a floating point value representing how many years that number
	of seconds represents.
      
    • 

      
  • 
	Using the above equations, you simply need to subtract the
	time that passed on the ship from the time passed on earth.
      
    • 
    

  






  
Challenge

  

    What if, instead of just launcing one of the children into space,
    these crazy scientists launched both?
    Likely, they would have tried to send two of the siblings off into
    space, but at different speeds.  Write a new function
    called compute_relativistic_age_difference, which computes
    the difference between two siblings who were launched into space
    at differing speeds.