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### Locating Pi on a Number Line

```
Date: 08/23/2000 at 13:26:17
From: Jennifer Reed
Subject: Locating pi on a number line

I need to find out how to locate pi on a number line. I have to show
it to the class. Can you tell me the best way to do this? What number
for pi should I use? I mean, how many places should I go to? Should I
just use 3.14, or should I go further?
```

```
Date: 08/23/2000 at 15:56:31
From: Doctor Ian
Subject: Re: Locating Pi on a number line

Hi Jennifer,

A common approximation for pi is 3.14, so you could just draw a number
line and label pi like this:

<---|---------|---------|---->
2         3         4
^
|
pi

But that shows where pi _is_, more or less. If you want to show how to
_find_ it, you might do this: Take a circle whose diameter is one, and
'set' it on a number line so that it rests on zero.

.
.       .

.           .

.       .
.
<---------|-------------------------->
0

Cut the circle at this point, and roll it out flat, so that one end
remains at zero.

.  .  .  .  .  .  .  .  .
<---------|------------------------------->
0                       ^
|
?

How far will the other end reach?

On the other hand, it's possible to compute pi by summing various
infinite series. For example, it's true that

pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...

which means that

pi = 4(1 - 1/3 + 1/5 - 1/7 + ...)

= 4 - 4/3 + 4/5 - 4/7 + ...

So you could draw a number line, start at 0, then move 4 units to the
right, then 4/3 units to the left, then 4/5 units to the right, then
4/7 units to the left, then 4/9 units to the right, ... and so on,
until you get tired or the class period ends.

-4/7<----
--------->+4/5
-4/3<-----------------
------------------------->4
<---------|------------------------------->
0

With each move, you jump past pi, so pi will always be between the
last two moves that you made. The more jumps you make, the closer
you'll get to the actual position.

-4/7<----
--------->+4/5
-4/3<-----------------
------------------------->4
---------|-------------------------------
0
[                        ]   pi is somewhere in here
[                ]         somewhere in here
[        ]                 somewhere in here
[   ]                 somewhere in here

I hope this helps. Be sure to write back if you have more questions,

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
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