Okay, granted, I am not a mathemetician or engineer, nor do I work in any vocation requiring me to use any type of math more complicated than algebra. Now, while I fully support the further advances of science (to an extent…don’t ask me about the space program), I have a question or two that have puzzled me for years. What is the practical application of computing pi to the umpteenth decimal place? While I understand that it is a non-repeating, non-terminating number, why doesn’t it repeat or terminate? And how was this discovered? And why bother computing it so far?
The master has spoken:
http://www.straightdope.com/classics/a3_357.html
>> What is the practical application of computing pi to the umpteenth decimal place?
0.000000000
>> why doesn’t it repeat or terminate?
Because it is completely irrational. No matter what you say to it, it just won’t listen. I much prefer more rational numbers but that’s just my preference.
>> And how was this discovered?
By Chinese mathematician Lin Piao in 1856. have you done a Net search? Tried Britannica perhaps?
>> And why bother computing it so far?
Some people don’t have girlfriends and don’t know what else to do.
sailor:
Yes, there is a use to computing pi to a large amount of decimal places. It’s called cryptography. Perhaps you’ve heard of it. Pi is a great source of long strings of random numbers, very useful in making keys and other things. The very act of computing pi can be used as a very handy benchmark for processors, as it is a known series of instructions.
Does it have to be pi? No, we could compute the value of e or the square root of seven or the fine structure constant and the numbers would be similarly useful. But, as with most things, pi is ensconced in tradition.
There is a great book called “A History of Pi” by Petr Beckmann. It marks the advance of civilization by examining not only how people computed the irrational little devil, but also by how various societies treated the people intelligent enough to do it.
A History of Pi at Barnes & Noble.com
sailor:
Yes, there is a use to computing pi to a large amount of decimal places. It’s called cryptography. Perhaps you’ve heard of it. Pi is a great source of long strings of random numbers, very useful in making keys and other things. The very act of computing pi can be used as a very handy benchmark for processors, as it is a known series of instructions.
Does it have to be pi? No, we could compute the value of e or the square root of seven or the fine structure constant and the numbers would be similarly useful. But, as with most things, pi is ensconced in tradition.
There is a great book called “A History of Pi” by Petr Beckmann. It marks the advance of civilization by examining not only how people computed the irrational little devil, but also by how various societies treated the people intelligent enough to do it.
A History of Pi at Barnes & Noble.com
Derleth, I am quite familiar with the topic of cryptography as you can see if you search some past threads about this topic. Can you please explain to me in more precise terms exactly what is the use of calculating PI for cryptography? Not a general affirmation but a concrete application.
Also, saying it serves as a benchmark for computers… well, by that definition anything is useful.
Q. What is the use of calculating <insert any number> to X significant digits?
A. It serves to know how fast we can calculate <same number> to X significant digits.
Gimme a break. I think the question implies quite clearly it is asking the use of calculating especifically PI() and not any other number. My answer is still that there is no practical use and Cecil agrees with me. Need I say more?
This is the only good PI story I know.
Some years ago I took a course in Business Anaysis. While discussing the point that one should not make jokes in documentation the lecturer showed an example. It was :
“Working storage fields may be used to store values so that they only need to be changed in one place. In this case the value is PI. So if the value of PI changes you only have to change it here.”
I laughed uproariously but no-one else did. I therefore thought that this was a very clever gag - if you got it, it was funny but didn’t refute the premise; if you didn’t get it you just carried on as normal.
I suggested to the lecturer that the author was a genius, he gave me THAT look, and …well we all know the rest.
In the end of the book, the value of pi, out to the umpteenth decimal place, contains code for the picture of a circle. This is supposedly representative of the mystical interweavings of the universe at work. Pi will eventually contain such things (it has to, it can’t repeat), but that is not the interesting part.
Now, certainly e or sqrt(7) could be similarly calculated, but neither is so elegantly derived from the natural world. (IIRC, e is really nothing but a convenient base to use for calculus, like radians for trig).
Maybe part of the “reason” for calculating pi is the coolness factor, the possibility of magic.
mystical interweavings of the universe?? Natural world? … Rene de What!!!
Isn’t e naturally occuring in decay graphs? I mean, in the real world. Bacteria and stuff.
There’s plenty of practical use if you’re a mathematician. Certain theoretical questions about the distribution of the digits in the decimal expansion of pi are still (to the best of my knowledge) unanswered. For example, do each of the ten digits occur with equal frequency, and what about each of the possible two-digit sequences, and so forth? More importantly, if they do occur with equal frequency then why? Studying the digits of pi may provide clues to these questions.
(And before anyone asks how an abstract mathematical problem is “practical”, let me remind you of Fermat’s Little Theorem, which is the core of the RSA encryption algorithm today but was pretty darn abstract in the 1600’s when Pierre de Fermat coined it. Sometimes you can’t predict what will become useful at a later date.)
Computing pi - Just say no.
It is useful for number theory, etc, as pointed out by Math Geek, but pi is not a source of random numbers, any more than the phone book is. The digits of pi are not random, by definition, because they are the digits of pi. They can be predicted and duplicated. Random numbers cannot.
If you currently use an application that uses pi for its random digits, then I strongly suggest you switch.
Hmm…which leads to the question of “what is random?”. If the digits follow no known pattern, yet are not random, what does random mean?
Not being duplicated doesn’t count. Give me any series of random numbers, and I’ll give you a formula to describe them (or rather, I won’t cos I can’t be bothered, but the method is simple, if tedious).
Math Geek, you can say exactly the same of any other irrational number. As has been said, in practical use, just the first few digits are more than enough. The OP says “What is the practical application of computing pi to the umpteenth decimal place?” and the answer is “None”. What you describe is not a “practical application”.
Pi was used as a means for the civilizations of Earth
and Mars to figure out each other’s languages. It was the
common starting point from which we extrapolated all else,
experiencing nothing but each other’s radio signals.
Before that, they could tell that the radio signals were
intelligent, but couldn’t begin to decipher them.
It’s serendipitous that Martians use base 10 also.
Actually, one of the less formal definitions of “random” is exactly what Joe_Cool suggested: a “random” sequence is one that can’t be duplicated by any algorithm shorter than the sequence itself (in other words, an algorithm that just which “predicts” the digits by using a big lookup table doesn’t count). Anything else is at best “pseudo-random”.
True, but pi is a wee bit more mathematically significant than, say, the square root of 81, and thus it tends to get studied more.
Well, as the latter part of my post indicates our opinions of what constitutes “practical” differ somewhat. But characterizing mathematicians who study the distribution of the digits of pi as people who just “don’t have girlfriends and don’t know what else to do” is rather ill-informed.
Okay, maybe this is closer to what I was actually trying to determine. Let me ask this: WHY is pi so darned mathematically significant that it has to be continually studied? I mean, it never ends, and never terminates. Big deal. Accept it, and move on.
I see I have touched a raw nerve here but I guess it was only to be expected from someone who calls himself Math Geek. Speaking just for myself, I find a having a girlfriend much more “practical” than having the umpteenth digits of PI, but that’s just me.
Re. the definition of “random”. I guess we could come up with several definitions but for the purpose of information and cryptography anything which can be calculated or known in any way is not random. Random would mean totally unpredictable. PI, like any other series, is not random. Far from it.
I seem to recall the governor of a Bible-belt state once got unduly mystical about trinities and sevens and such and issued an edict that set the state’s official value of * to 3. Of course, it was substantially ignored by anyone with any reason to utilize *; meanwhile, the population of people who shared the governor’s regard for threes and sevens–the natural constituency in support of his pronouncement–by and large had no idea what he was talking about and also ignored the matter, so it does not appear to have won him any praise or brought any trinitarian influence to bear on godless mathematics. Which just goes to show that you cannot have your pi and edict too.