Pi in Real LifeDate: 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 |
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