Assignment 1. Variables, Expressions, Statements and Functions


The Way of the Program

Exercise 1

  1. In a print statement, what happens if you leave out one of the parentheses, or both?
  2. If you are trying to print a string, what happens if you leave out one of the quotation marks, or both?
  3. You can use a minus sign to make a negative number like -2. What happens if you put a plus sign before a number? What about 2++2?
  4. In math notation, leading zeros are ok, as in 02. What happens if you try this in Julia?
  5. What happens if you have two values with no operator between them?

Exercise 2

Start the Julia interpreter and use it as a calculator.

  1. How many seconds are there in 42 minutes 42 seconds?
  2. How many miles are there in 10 kilometers? Hint: there are 1.61 kilometers in a mile.
  3. If you run a 10 kilometer race in 42 minutes 42 seconds, what is your average pace (time per mile in minutes and seconds)? What is your average speed in miles per hour?

Variables, Expressions and Statements

Exercise 1

  1. We’ve seen that n = 42 is legal. What about 42 = n?
  2. How about x = y = 1?
  3. In some languages every statement ends with a semi-colon, ;. What happens if you put a semi-colon at the end of a Julia statement?
  4. What if you put a period at the end of a statement?
  5. In math notation you can multiply x and y like this: x y. What happens if you try that in Julia?

Exercise 2

Practice using the Julia interpreter as a calculator:

  1. The volume of a sphere with radius r is 4/3 π r3. What is the volume of a sphere with radius 5?
  2. Suppose the cover price of a book is $24.95$, but bookstores get a 40% discount. Shipping costs $3 for the first copy and 75 cents for each additional copy. What is the total wholesale cost for 60 copies?
  3. If I leave my house at 6:52 am and run 1 mile at an easy pace (8:15 per mile), then 3 miles at tempo (7:12 per mile) and 1 mile at easy pace again, what time do I get home for breakfast?

Functions

Exercise 1

Write a function named right_justify that takes a string named s as a parameter and prints the string with enough leading spaces so that the last letter of the string is in column 70 of the display.

right_justify('monty')
                                                                 monty

Hint: Use string concatenation and repetition. Also, Julia provides a built-in function called length that returns the length of a string, so the value of length("monty") is 5.

Exercise 2

A function object is a value you can assign to a variable or pass as an argument. For example, do_twice is a function that takes a function object as an argument and calls it twice:

function do_twice(f)
    f()
    f()
end

Here’s an example that uses do_twice to call a function named print_spam twice.

function print_spam()
    println("spam")
end

do_twice(print_spam)
  1. Type this example into a notebook and test it.
  2. Modify do_twice so that it takes two arguments, a function object and a value, and calls the function twice, passing the value as an argument.
  3. Copy the definition of print_twice from the lectures to your notebook.
  4. Use the modified version of do_twice to call print_twice twice, passing "spam" as an argument.
  5. Define a new function called do_four that takes a function object and a value and calls the function four times, passing the value as a parameter. There should be only two statements in the body of this function, not four.

Exercise 3

Note: This exercise should be done using only the statements and other features we have learned so far. Write a function that draws a grid like the following:

+ - - - - + - - - - +
|         |         |
|         |         |
|         |         |
|         |         |
+ - - - - + - - - - +
|         |         |
|         |         |
|         |         |
|         |         |
+ - - - - + - - - - +

Hint: to print more than one value on a line, you can print a comma-separated sequence of values:

println("+ ", "- ")

println advances to the next line, but print doesn't:

print("+ ")
println("- ")

The output of these statements is "+ -" on the same line. The output from the next print statement would begin on the next line.

Write a function that draws a similar grid with four rows and four columns.

Interface Design

Exercise 1

  1. Draw a stack diagram that shows the state of the program while executing circle(🐢, radius). You can do the arithmetic by hand or add print statements to the code.
  2. The version of arc in the lectures is not very accurate because the linear approximation of the circle is always outside the true circle. As a result, the Turtle ends up a few pixels away from the correct destination. My solution shows a way to reduce the effect of this error. Read the code and see if it makes sense to you. If you draw a diagram, you might see how it works:
""" Draws an arc with the given radius and angle.

    t: Turtle
    r: radius
    angle: angle subtended by the arc, in degrees
"""

function arc(t, r, angle)
    arc_length = 2 * π * r * abs(angle) / 360
    n = trunc(arc_length / 4) + 3
    step_length = arc_length / n
    step_angle = float(angle) / n

    # making a slight left turn before starting reduces
    # the error caused by the linear approximation of the arc
    Turn(t, -step_angle/2)
    polyline(t, n, step_length, step_angle)
    Turn(t, step_angle/2)
end

Exercise 2

Write an appropriately general set of functions that can draw flowers.


In [33]:
using TikzPictures
TikzPicture(L"""
    \draw (0,0) arc (0:-60:2) arc (180:120:2);
    \draw (0,0) arc (60:0:2) arc (240:180:2);
    \draw (0,0) arc (120:60:2) arc (300:240:2);
    \draw (0,0) arc (180:120:2) arc (360:300:2);
    \draw (0,0) arc (240:180:2) arc (60:0:2);
    \draw (0,0) arc (300:240:2) arc (120:60:2);
    \draw (5,0) arc (0:-60:2) arc (180:120:2);
    \draw (5,0) arc (30:-30:2) arc (210:150:2);
    \draw (5,0) arc (60:0:2) arc (240:180:2);
    \draw (5,0) arc (90:30:2) arc (270:210:2);
    \draw (5,0) arc (120:60:2) arc (300:240:2);
    \draw (5,0) arc (150:90:2) arc (330:270:2);
    \draw (5,0) arc (180:120:2) arc (360:300:2);
    \draw (5,0) arc (210:150:2) arc (30:-30:2);
    \draw (5,0) arc (240:180:2) arc (60:0:2);
    \draw (5,0) arc (270:210:2) arc (90:30:2);
    \draw (5,0) arc (300:240:2) arc (120:60:2);
    \draw (5,0) arc (330:270:2) arc (150:90:2);
"""; options="very thick, scale=3, transform shape", preamble="""
    \\usepackage{newtxmath}
    \\renewcommand{\\familydefault}{\\sfdefault}
""")


Out[33]:

Exercise 3

Write an appropriately general set of functions that can draw following shapes.


In [68]:
using TikzPictures
TikzPicture(L"""
    \draw [turtle={home,right=36,forward,left=126,forward=2.351141cm,left=126,forward,left=144}];
    \draw [turtle={home,right=72,right=36,forward,left=126,forward=2.351141cm,left=126,forward,left=144}];
    \draw [turtle={home,right=144,right=36,forward,left=126,forward=2.351141cm,left=126,forward,left=144}];
    \draw [turtle={home,right=216,right=36,forward,left=126,forward=2.351141cm,left=126,forward,left=144}];
    \draw [turtle={home,right=288,right=36,forward,left=126,forward=2.351141cm,left=126,forward,left=144}];
    \begin{scope}[xshift=6cm]
        \draw [turtle={home,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
        \draw [turtle={home,right=45,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \draw [turtle={home,right=90,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \draw [turtle={home,right=135,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \draw [turtle={home,right=180,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \draw [turtle={home,right=225,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \draw [turtle={home,right=270,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \draw [turtle={home,right=315,right=22.5,forward,left=112.5,forward=1.530734cm,left=112.5,forward}];
    \end{scope}
"""; options="very thick, scale=2, transform shape, turtle/distance=2cm", preamble="""
    \\usepackage{newtxmath}
    \\renewcommand{\\familydefault}{\\sfdefault}
    \\usetikzlibrary{turtle}
""")


Out[68]:

Exercise 4

Read about spirals at http://en.wikipedia.org/wiki/Spiral; then write a program that draws an Archimedian spiral (or one of the other kinds).