Lab 2

Topics

1. Basic arithmetic operations and expressions
2. "Casting" types (converting values from one type to another)

To get started, create a directory called lab02 inside your cs5001 directory.

Programming exercises

1. Click hereLinks to an external site.open in new window to go to Weather Underground for Seattle, WA. This website compiles a variety of climate data such as high and low temperatures, pressure, visibility, precipitation, etc.

   Use the data provided on this website to perform arithmetic computations using the four operators: +, −, ∗, and /. Create a program called weather.py which calculates the following and prints out the results (you can enter the input values into your program by hand):

   • What is the difference between the highest and the lowest temperature values predicted for the 10 day forecast?
   • What is the average temperature at noon predicted for the 10 day forecast?
   • What is the highest temperature predicted for the 10 day forecast, converted from Fahrenheit to Celsius?

2. Using input you can prompt the user for input on the command line. Write a program called adder.py which takes input from the user in the form of numerical values, and prints out a sentence reporting the sum of the values, like this:

 tmullen$ python adder.py
 Enter a first value: 5
 Enter a second value: 6
 The sum of 5 + 6 is 11

Make sure that the + operator treats your numerical values as integers where necessary, but that it concatenates strings appropriately where it should. The numerical values you input on the command line will be strings, and you'll need to cast them appropriately to do arithmetic operations on them. Use the appropriate built-in type constructor (listed hereLinks to an external site.open in new window) to create values of the appropriate types.

3. Defining functions is a way to organize the behavior of a program. One useful approach to encapsulating a program's behavior is to define a function called main containing the program's instructions, and tell Python to call this function as soon as it executes the program. Try this with your adder.py code. Refactor your adder so that it is called from within the body of main, shown below. The code as written will run but it won't do anything. pass is a special word in Python that does nothing, but ensures that Python regards a single line indented block as syntactically acceptable (without pass here, this would be a syntax error).

   The code following the # sign is comment code. Any time the # appears in a python program, the interpreter simply ignores everything to the right of the symbol until the end of the line. So you can write human-readable comments that are ignored by the program.

 def main():
     pass # Delete the 'pass' and replace it with your code

 main() 

4. You can call the program in the same way you did previously. It should behave exactly like the previous version of the program behaved.

5. Write a program called euclidean_distance.py that prompts the user for four numerical values representing two 2-dimensional points (so, x1, y1, x2, and y2) and then calculates the Euclidean distance between the two points using the Pythagorean theoremLinks to an external site.open in new window.

   You'll need to calculate square roots. This is possible to do in a couple of ways. You could use ** (the exponentiation operator) to the power of 0.5. This may not be the most readable and intuitive way to represent square roots, though. I'd recommend using sqrt() from the mathLinks to an external site.open in new window library. In order to do this, you'll need to call import math at the beginning of your program. Read the Python docs for more details about math.

   As in the previous example, wrap this code in a main function, and call it with main() at the bottom of the code.

6. For a bit more practice reading the docs for math, write a program called trig_functions.py that prompts the user for an angle in degrees, and prints out the sine and cosine valuesLinks to an external site.open in new window for the angle. Don't calculate/derive these by hand, that's what computers are for! Use the built in functions in math to calculate the answers for you based on the angle. Once again, wrap your code in a main function and call it with main().

   Below are some sample correct inputs and outputs. Make sure you test your program on these values to make sure the solution is correct.

 tmullen$ python trig_functions.py
 Enter an angle: 0
 The cosine of 0.0 is 1.0
 The sine of 0.0 is 0.0
 tmullen$ python trig_functions.py
 Enter an angle: 90
 The cosine of 90.0 is 6.123233995736766e-17
 The sine of 90.0 is 1.0
 tmullen$ python trig_functions.py
 Enter an angle: 45
 The cosine of 45.0 is 0.7071067811865476
 The sine of 45.0 is 0.7071067811865475

But wait a minute! The cosine of 90 is zero! Why is Python telling us that it's 6.123233995736766e-17? What does that even mean? First, the notation. Python uses scientific (exponent) notation by default for very large and very small numbers. Exponent notation consists of a number followed by e, followed by the power of ten necessary to represent the intended value. For example, if we type the following values into the Python REPL console:

 >>> 5e+0
 5.0
 >>> 5e-0
 5.0
 >>> 5e+1
 50.0
 >>> 5e-1
 0.5

These can be read as "five times 10 to the power of...". The first two cases are both zero (10 to the power of zero is 1). The second two cases 5 times 10 and 5 times 10 to the power of -1 (i.e. 5/10).

So we can now see that 6.123233995736766e-17 is a very small number. In fact, it's approximately zero, and it's the number that Python arrives at when it uses the math library's cosine function on 90 degrees (pi/2 radians). The problem in this case is the approximation of pi that Python uses.

This underscores a sometimes inconvenient truth: Computers deal with finite, fixed approximations of numbers. They don't deal directly with real numbers. When dealing with real numbers, we often need to make choices about the degree of precision we are interested in. If you need to test for a zero-valued cosine in a program, for example, you might need to specify some very small value and assume that if the result is less than this value it is close enough to zero for your purposes.

Submission

Make the usual commit to GitHub, and upload weather.py, adder.py, euclidean_distance.py, and trig_functions.py to Canvas.

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