# HW1: Calculate the Square Root of a number¶

This assignment is designed to start you using your brain to think logically (and clearly). There is no “right answer” to this one, each of you might come up with something different (or nothing at all if it stumps you, hopefully that will not happen. Send me email if you get stuck!) You will submit a simple text file with your solution to Blackboard. Use something like Microsoft Notepad until you get a good programmer’s editor set up, but do not use Microsoft Word for anything in this course.

Warning

You will soon discover that you really do need to read assignments carefully, especially in this course. Do not go off and start working on a solution until you are sure you understand the problem. Many (most) students get so focused on the example shown here, that they miss the fact that this is a general problem, not just the one shown in the example!

Note

You will need to upload lab work using BlackBoard. To do this, open up the “Lab assignments” page. You will see this lab assignment there. When you are ready to submit your work, click on the Lab title. You will be taken to a page where you can upload one or more files. I would make sure all files you need to submit are in the same folder, and use “Control-Click” to select all files at once. When you are happy with the selection, click on submit.

You will have one file to upload this week: SquareRoot.txt

Note

Blackboard will allow you to submit work for three attempts. Normally, you only get to submit a second (or thind) attempt after I review your first attempt. I will tell you what needs attention for a resubmit.

## What does this mean?¶

```
x = sqrt(5)
```

Note

This assignment is not about programming, so do not attempt to write anything looking like a program (if you know how to do that, based on previous studies). Instead, this is a thinking problem.

In addition, this assignment is not just trying to calculate the square root of 5. The number you may be asked to work with could be any number (except a negative one). not negative?)

If you own a calculator, you can probably figure this out. The `sqrt`

thing
is called a `function`

. A `function`

is a magical gadget that can do some
work for you. We do not need to know how this magic happens most of the time,
that is what the calculator is for. But what if you needed to design the
calculator. How will you get the magic to happen?

You should have run into these function things in your math classes. How you
get out the actual value for `x`

without using a calculator was probably left
as a puzzle for you to figure out. Let’s try to do that here!

### Back to your math class¶

You probably saw something like this in your math text:

This is an `equation`

. The two things on either side of the `=`

symbol are
supposed to be `equal`

. (That is why we call it an `equal symbol`

- DUH!)
You were probably also told that if you figured out the right value for the
`x`

thing, this equation would be true as well:

Now, most computers cannot generate that funny little `2`

in that equation,
so we will show it this way instead:

Now we have another problem. Many math books show things this way, but how do
we really know that `xx`

means `x times x`

? (I know, you saw it written
this way a lot, and the symbols were always one character long.) We will solve
this problem by using a new symbol for multiplication (no, we will not use
`x`

that would really get confusing. Instead, we will use a star: `*`

. So
that last equation would look like this:

```
x * x = 5
```

That `*`

symbol means `multiply`

. Got it all figured out now?

The question we want to address in this lab is simple.

```
How do we go about figuring out the right value for "x"?
```

### Your problem¶

Suppose you have a basic four-function pocket calculator that can only do addition, subtraction, multiplication, and division. How would you approach figuring out the answer? Think about this, and try to come up with a scheme that will give you the answer. Do not just use simple trial and error, think about how you might get an accurate answer. You might start off with a one digit guess, like 2 or 3, then add a digit after the decimal point to refine your guess. Your calculator will help you check your guesses.

It might (should) occur to you that you need some way of telling if your guesses are getting better, or worse. Also, you need a way to decide when you are done, your answer is “good enough”. That might be when you have five decimal places to the right of the “dot”. You get to decide for now.

No fair just turning to Google to find the scheme. You need to start thinking problems through by yourself. So do your own thinking about this, remembering that we are trying to teach a computer how to do the work. The goal is to produce a list of the steps needed to figure out the right value for “x” using just the multiply key on the calculator

Note

If you do not happen to own a calculator, there is one on your computer. Go
to `Start -> All Programs --> Accessories --> Calculator`

. (There will
be a square-root key on that calculator. You may use it only to see what
the right answer is, not to figure out the answer.

Warning

This is not a programming exercise, it is a thinking exercise. You will need to use some kind of trial-and-error process to get the answer. To help in thinking up a scheme, try thinking about this problem (it is similar to what you need, only totally different in what you want to accomplish):

Suppose you need to back a truck up to a trailer so you can drop the hitch onto the ball on your truck. How would you do that. (Assume that all you need to do is move forward or backward to get things right!)

#### Produce a requirements list¶

From the lecture this week, produce as simple a requirements list as you can for this problem. Be sure to read through the rest of the assignment, there are a few requirements left to identify in what follows. You can simply add those additional requirements to the requirements you derive fro the above general problem statement.

#### Produce a set of instructions¶

Write your solution as a set of sentences that tell the user what to do to get the answer. Pretend the person who is going to follow your instructions is your poor mother, who does not know much about all this stuff. (Of course, if your mother is a Rocket Scientist (I am one, by the way!), you may need to think up some other person - HA!)

### Checking your work¶

After you write down the process you came up with clearly enough that another person could use your process to figure out the answer, practice by following your own steps exactly. This is hard to do when you wrote them down, since you “know” what you meant. Remember that someone else will not have that knowledge and will do something you never expected. (Silly people). They will do what you say to do, not what you mean for them to do. (Some times they will even do things you did not say to do! Arrrgh!) When teaching a dumb computer to do your work, trust me, it will never do what you mean, only what you say!

To make sure your scheme works on general problems, try it out on some number other than 5, say 35 for example! Even worse, try it on 10,000.456! Do you think this will really work?

### What to turn in¶

Once you think you have a solution, write it up using short numbered sentences that explain what you need to do. Nothing fancy is required, do the best you can. We are learning new stuff here, so try to be clear.

Save your work in a file named “SquareRoot.txt”. If you named it something else, you can rename it before turning it in.

At the end of your instructions, show how your scheme works on some example problem (probably not 10,000.456).

Hopefully, your values will be getting better and better. If not, do not worry about it for now, but you might think about why this is not working they way you wanted it to!

## What to Submit¶

Upload the one file: “SquareRoot.txt” to Blackboard.

## When is This Due?¶

Assignments are due on Sunday of the week assigned for full credit.

Note

Unless explicitly told otherwise, all work you submit for this course must be produced using a simple text editor. All files submitted for grading must be produced using the editor you use to create program code. I will go over one such tool, gVim, but you are free to use any editor you are comfortable as long as it produces simple ASCII text files. See me if you have questions about any tool you want to use.