I've always told students, "
You should use at least three different sources when studying a
particular subject, since you may, 1) have trouble understanding what one author says at times,
or 2) wish to verify some questionable 'facts' presented by someone. But when trying to
verify the validity of a number, use as many reliable sources as possible! "
The CAD server which contained the erroneous Pi file at UCLA was shut down quite some time ago (see below); if you find a copy on any other server at UCLA please let me know. The emphasis here is still the same: You should always verify data found on the Net (especially numerical data), no matter where you find it; you'll soon see why!
Many years ago, while clicking a link at YAHOO
searching for Pi values, we came across a link that was
(and finally no longer is) on this page:
Back then, the page looked similar to this:
|Home > Science > Mathematics
> Numerical Analysis > Numbers > Specific Numbers > Pi >|
appeared as the best choice for most people when compared to the millions and
billions of digits above it.]
But the value stored there was
all wrong after the first 15,093 decimal digits!
(After sending various people at UCLA e-mails for about 5 years, we got tired of never getting a single reply AND never finding a correction to the site; let alone a correction with a note explaining why they revised it... something we'd logically assume they'd have to do. Instead, after some months of people telling us they could no longer access the file, we finally concluded this particular server at UCLA had been shut down permanently [ which, highly likely, was due to some hardware issue; I doubt it was because of this Pi error, but can't rule it out completely. ]. Obviously, since the whole server was gone, there would never be a need for UCLA to explain why this faulty Pi file had ever been there! So, they 'saved face' either way! )
The file itself had been clearly dated on the server as: 27-Jun-93 16:24 117k
and with YAHOO's and GOOGLE's help (and possibly other search engines of that time), the world had been served up this erroneous value for MANY YEARS.
Quite some time back, The Yahoo Directory for "Pi Digits" was down to only three links; ours was third on the list! On March 21, 2006, it had looked similar to this (and yes, as of February 1, 2011, this links are all still active!):
Science > Mathematics > Numerical Analysis > Numbers > Specific
Numbers > Pi > Decimal Digits
These files correspond to:
So, why does this still (even in 2011) concern me? Because many unsuspecting students had already copied this file thinking they could trust it! On the other hand, it may teach someone who stumbles across my page here, that 'you should never trust un-verified numerical data! ' As a matter of fact, trying to put a positive spin on my experiences while sending e-mails to UCLA, I had even speculated that this might be some kind of test by a professor there to see if his students understood what it meant to acquire VERIFIABLE information. But now I'm quite sure that wasn't the case! It was just a mistake someone made, perhaps by a student who never learned the necessity of checking for errors or even a university employee, and it was never corrected. Unfortunately, there are now many other web sites which have copied the same erroneous data, and that's one reason why this page still exists: To show you how to identify these erroneous Pi digits!
in the file were verified in many different ways; comparing it to a number
of reliable sources elsewhere. Would it surprise you to know that word
processors (if fast enough) were helpful in doing this? (Though anyone
with a sufficient knowledge of perl could also write a script
file to remove all the unwanted blank spaces and line feeds too.) The first
step in running a digital comparison with other Pi files, was to use a word
processor to remove all but the actual digits of Pi. For example, there were
18,333 spaces and 1,667 UNIX-style linefeeds which we removed from the file
from UCLA. And we always got the same results every time: Only the first 15,093
decimal-digits (of the supposed 100,000) were correct!
Furthermore, by making use of Pi-digits search programs, we verified that the digits which follow the location where this file does not match with the correct values is not due to someone jumping past one, two, or however many correct digits and then entering the rest of them: In other words, this is not a case of 'missing digits'; with the remaining digits merely being shifted 'out of position.' As proof, we've searched for various strings of digits which followed that location, and none of the chosen strings can be found anywhere within a reasonable location! Not even a string as short as these 10 digits: 7082898187 (which begins at digit 15,111 into the erroneous file) was found anywhere in the first 200,000,000 digits of Pi.
You can also perform such tests on files like this yourself, by looking at the 252nd-line of decimal digits where the errors first occurred (we've underlined the last good digit, the 15,093-rd, while showing the beginning of the incorrect digits in red here):
ResultsThe string 73884266 was found at position 15093 counting from the first digit
after the decimal point. The 3. is not counted.
The string and surrounding digits:
79866205734083757668 73884266 40599099350500081337
This page was brought to you by David G. Andersen [ WWW ] [Email]
Return to the Pi-Search Page.
this query took 0.001799 seconds to process
I've 'highlighted' the digit-position (15093) for you, and you can clearly see that the digits following the 73884266 all agree with those from verified files; not the one in question.
If you read Mr. Andersen's initial page, you'll find that he also verified the Pi files that he uses. Note that our use of his program is not meant to imply that I ever verified all of what used to be a 50,000,000-digit database, and was doubled on Pi day; 14 March 2001, to 100,000,000 digits and at this time is now 200,000,000 digits(!) by Mr. Andersen. (I would like to state though, that I've never found a single discrepancy between his digits and any from the sources we've used here and occasionally checked against his site.) As stated above, this was just a quick method to show other files independent of my own did not match the file in question at UCLA. A much more rigorous method of digitally comparing every single byte from numerous sites containing 'officially' VERIFIED Pi files was used in creating the Pi files for The Starman's Realm!
(You can also check the list below* for other Pi files we verified as being accurate.)
You'll find our own 100,000 digit text file of Pi here:
PI.100.000.TXT -- 100,000 Decimal Digits of Pi.
(Each block of 1000 digits is clearly labeled with 50 digits per line; each line being composed of five 10-digit strings. I've even included the next 50 digits AFTER the 100,000-th digit so there's no question about whether the last digit was rounded off or not.) Our Pi Files Download Page also lists some of the sources which we've used to VERIFY the Pi files here.
If you enter the sequence reference number of A000796 into the search form on this page: http://oeis.org/, you'll be presented with a page that lists on-line references to the "Decimal expansion of Pi." About half-way down you'll see LINKS and a reference to our web site's Pi Pages:
which used to end with the following statement:
Mr. Marshall and I did exchange an email at one time about the fact that he couldn't make a connection with the cad.ucla.edu server; apparently he forwarded the data about my web site to Neil Sloane. I can only assume that N.J.A. Sloane, the "Integer Sequences" author, decided to drop the comments (shown above in red) some time later; and the link to the defunct UCLA server was later dropped when it was found to longer exist.
The Starman. Updated/Checked links on:
Wednesday, February 2, 2011.
Last Update: Tuesday, March 21st, 2006.
Updated: (added note about the "Encyclopedia of Integer Sequences"):
Tuesday, December 17th, 2002.
Revised: December 7th, 2003.
The Starman's Pi Files page
The Starman's Math page