# Session 6: Distance Measures - Module B: 1D and 2D

## 1. Discussion: Computing Distances

Running from a zombie. (Distances on a line.)

What if we have a 2 dimensional plane?

## 2. 1D Distance Code

I've written a program to calculate distances in one dimension.

- Save
**1Ddistance.py** to your programs folder.
- Open the code up in gedit and take a look at it.

Find the line where the distance is calculated. How does it compare with the formula we discussed earlier?

Try running the program so you get a feel for how it works:

- Open a terminal window.
- Change the directory to your programs directory:

`cd programs/`

- Start IPython with the command:

`ipython`

- From IPython, run the program:

`run 1Ddistance.py`

- Now that the program is loaded you can try more values by simply calling the function in ipython with different values.

`distance1D(7,13)`

- Try more values, but remember if you change the program in gedit you need to rerun it in ipython (step 4).

## 3. 2D Distance Code

Now you can make the program a little more useful by converting it to compute distances in two dimensions!

First, save a copy of the program so you still have the original:

- Click
**File** in the lefthand corner of gedit, then choose **Save as...**.
- Save the program as
**2Ddistance.py**.

You're ready to change the code so that it calculates the distance between two points in a two-dimensional plane.

- You will need to add two new variables for the y coordinates of the two points as parameters. Make sure they have different names than the ones already there!
- Then you'll need to change the distance calculation line to use the formula for two-dimensional distances.

There are a couple things you'll find useful:

- To square an expression in Python, type
`x**2`. This works either for a single variable like x, or more complicated expressions like x + y. Ex: `(x + y)**2`
- To find the square root of an expression, type
`sqrt(x)`. Like squaring, this can also have a more complicated expression passed in.

Run your program in IPython to test it. If you use (x1, y1) = (1, 1) and (x2, y2) = (4, 5), your program should print 5.0 for the distance.

Once you have the distance calculation working, uncomment the last line of the program by erasing the hash symbol to generate a plot to go with your distance calculation.

Remember to save your favorite plot and answer these questions on your webpage!