Pi in Real Life

Date: 7/1/96 at 12:34:6
From: Ian Ralph
Subject: help

My name is Ian and I'm a teacher from High Wycombe Primary School 
W.A. We have just covered circumference of circles and pi. The 
children asked how this concept is used in real life, i.e. 
engineering, etc., and I had a devil of a time thinking of one. 

Also what / who is pi named after?
Any help would be appreciated.

Thanks
 "Pestered"

Date: 01/04/97 at 14:59:02
From: Doctor Keith
Subject: Re: help

Hi,

I love "how is this used" questions, since I am an engineer.  Pi is
an often-used number, but here are some general categories with
examples:

Geometry problems: drawing, machining, etc.

  For instance, I used to work on fighter jets before I went back to 
  get my Ph.D., and we would frequently need to calculate areas of the 
  skin of the aircraft or arc lengths, for everything from fitting 
  equipment in, to line-of-sight calculations.  Additionally, pi comes 
  up in machining parts for aircraft; for instance, you might need a 
  circular slot for mounting a camera that has a certain radius and a 
  certain arc length.

Signals: radio, TV, radar, telephones, etc.

  You have probably heard of sine waves. Well, sine waves have a 
  fundamental period of 2*pi, so pi becomes vital in signal 
  processing, spectrum analysis (finding out what frequencies are in a 
  wave you receive or send), etc.  
  A neat example of this is listening to peoples' voices and rating 
  them from high to low (bass).  Then if you have access to a computer 
  with a microphone and a sound player with a graphic display of the 
  sound, you can take a sample of the voices and play them back in a 
  sound player and watch the graph. Check to see if your guesses were 
  right.  The frequency plot that they are showing when the sound plays 
  is actually used by engineers to do such things as decide sampling 
  rates, ideal processing of the sound, etc., and the graph is usually 
  in multiples of 2*pi.

Probability: estimation, testing, simulation.

  Everyone's favorite distribution (normal or Gaussian) has pi in the
  formula, and it is used in all areas of engineering to simulate 
  unknown factors and loading conditions.  One example is what is 
  called "white noise," which is a normally distributed random variable 
  used in estimation to predict such things as wind gusts on a plane or 
  the worst case vibrational loading on a beam (this is a really big 
  use of pi).  White noise is also used to give a certain amount of 
  apparent "bumpiness" in many software simulations such as games.

Navigation: global paths, global positioning.

  When planes fly great distances they are actually flying on a arc
  of a circle. The path must be calculated as such in order to 
  accurately gauge fuel use, etc.  Additionally, when locating yourself 
  on a globe, pi comes into the calculation in most methods.

Plenty of other areas exist, but I thought these would probably be the 
most easily understood by students.  If you need additional info let 
us know--we are here to help.  

Pi is named after the Greek letter pi, which is the symbol we use for 
it.  I have checked my math history book, and the original discoverer 
of pi is not known, but it was used by the ancient Egyptians, Greeks, 
Hebrews, and Babylonians.

Many mathematicians have played with it and have improved the 
approximation that we have.  Some examples are:

  Babylonian (1800-1600 BC):      pi  ~  3
  Hebrew     (1 Kings 7:23):      pi  ~  3
  Egypt      (Rhind Papyrus):     pi  ~  3 1/7

All of these are approximations, as they are measures of real near-
circular objects (a large metal bowl in the Hebrew case, the volume of
a cylindrical grain silo for the Egyptian reference) which would
never be perfectly circular due to manufacturing considerations, 
measurement techniques, etc., but they served as useful approximations
to do the necessary work.  Thus such things as the volume of a can for
packing things, or the area a water sprinkler can water, involve pi.
It's everywhere!  

Good luck.

-Doctor Keith,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 02/04/97 at 18:53:54
From: Doctor Ken
Subject: Re: help

Hi -

I was just going through some old questions and answers, and found 
this one. Here's another tidbit for your cranium: you might ask why we 
chose Pi as the letter to represent the number 3.141592..., rather 
than some other Greek letter like Alpha or Omega.  Well, it's Pi as in 
Perimeter - the letter Pi in Greek is like our letter P.

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: Sun, 7 Sep 1997 10:11:43 -0500
From: Anonymous

Doc,

I used your site to help me confirm a simple formula that my failing 
memory simply lost a pointer to: the definition for circle 
circumference! In return, here's some more about how pi is used in 
the real world:

I bought a ski boat this year, and my front-wheel drive minivan has a 
tough time pulling it out of some of the sandier, wetter, and steeper 
boat launches; there simply isn't enough weight on the front tires in 
some cases to get good traction.  It won't entirely fix my problem (a 
4WD is in my future), but it will help (perhaps only marginally) to 
get slightly larger tires.

The problem with getting larger tires is that you change the outer 
diameter (circumference) of the tire, changing both the speedometer 
and odometer readings.  One annoyance of passenger tires is that the 
sizes mix American and metric measurements.  Most passenger tires, 
including my minivan, have a tire size like P195 75R15, where the 'P' 
is for passenger (as opposed to cargo), the 195 is the size, in 
millimeters of the width of the tire (face that meets the pavement), 
the '75' is the aspect ratio (percentage of profile or sidewall 
height of tire, given the width number), the 'R' signifies inner 
radius, or wheel radius size to mount on; and the '15' is this inner 
radius of the tire, in inches. So, inner diameter of tire in inches, 
width in millimeters, sidewall height a percentage of the two.

The tire shop suggests that a P205 70R15 will give me that extra 
centimeter of tread (not much, huh?), and come closest to not 
affecting the speedometer and odometer readings of my P195 75 R15.  
That is, a 205mm width tire with a 70% profile is 'close enough' 
to a 195mm width tire with a 75% profile. Is he right?

I spend a few minutes on the net getting some metric/American 
conversion formulas, heat up the left lobe a bit, and get an answer. 
A couple of constraints are that: 1) the only practical aspect ratios 
available for my vehicle are 60, 70, and 75; and 2) tire widths are 
available only in 10mm increments - 195, 205, 215, 225, etc...

Turns out, he's right. What I really want is a 208.9mm tire with a 
70% aspect ratio, OR a 205mm tire with a 71.3% aspect ratio, neither 
of which is available, so the 205mm 70  is closest.  The exact 
formula I come up with is aw=146.25; where a = aspect ratio and 
w = tire width.

How close is it?  I run a few more numbers and find that it's not 
bad: at 65MPH, my speedometer will read 65.3MPH, and at 70MPH, it 
will read 70.3MPH - off by far less than what I can actually read. 
And, over the next 50,000 miles, the odometer will actually show 50, 
225 - an extra 225 miles. Again, somewhat negligible.

So there you have it!  Without pi, I would have had to trust the 
garage mechanic, something I always try to avoid!

- raz, Eagan, MN