Sponsoring website: Emergency Boot CD

 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 toverify the validity of a number, use as many reliable sources as possible! "

# An Example of Why you should never trust Unverified Values from any site on the Net

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:
http://dir.yahoo.com/Science/Mathematics/Numerical_Analysis/Numbers/Specific_Numbers/Pi/Decimal_Digits/
Back then, the page looked similar to this:

 Home > Science > Mathematics > Numerical Analysis > Numbers > Specific Numbers > Pi > Multiple Digits of Pi - 5 million, 10 million, 100 million, and 200 million digits. 1,250,000 Digits 10,000 or 50 Million Digits of Pi - also 10,000 or 30 million digits of 1/Pi. 4,200,000,000 Digits of Pi and 1/Pi --- for serious number crunching! Pi to 100,000 Digits <--- [This was the faulty file which, unfortunately,   appeared as the best choice for most people when compared to the millions and    billions of digits above it.]

Entering the word "pi" and the number "3.14" in major search engines at that time, was highly likely to cough up a link to the UCLA CAD server; which was supposed to have 100,000 digits of Pi. For example, if you entered: "ucla pi = 3, 14159 26535" in GOOGLE.com, you'd get only one page which listed at the very top:

 Untitledpi = 3, 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 ... cad.ucla.edu/repository/useful/PI.txt - 101k - Cached - Similar pages

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!):

 Directory > Science > Mathematics > Numerical Analysis > Numbers > Specific Numbers > Pi > Decimal Digits 100,000 Digits of Pi - By Michael Huberty. [99,999 decimal digits and the last 3 are in error -- The Starman] Pi Files Download Page - 1,000 to 1,250,000 decimal places of pi, MD5 checksums for various lengths of pi, and pure ASCII pi decimal digit MD5 sums. thestarman.pcministry.com/math/pi/picalcs.htm     [This is our web site; we we're 2nd in 2006.] Pi to 1,000,000 Places - Care to count them all? [We did find an honest 1,000,000 decimal digits of Pi here, ending with the same exact digitsas our file: "106105779458151", but you'll have to spend some time figuring out how toaccess them! - The Starman.] 10,000 or 50 Million Digits of Pi - Also 10,000 or 30 million digits of 1/pi. [Years later; the links are still broken to all but the two 10,000-digit files! - The Starman]

 These files correspond to: 1) http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html; probably created with      a Pi calculation program, since the last three digits ("541") are in error. They should      read: 464 (and the 100,000-th decimal digit is a 6 ). This is an example of why you must     always carefully check the end of any Pi file, since most programs will be incorrect there! 2) Our web site (by The Starman; the link above is to one of our various mirror sites). 3) This author had 'bandwidth problems,' so he 'hides' the digits of pi to casual observers! 4) http://www.cecm.sfu.ca/projects/ISC/data/pi.html; reliable, but all links, except for     the mere 10,000-digit files, are still broken!!! The last digit in their 10,000-digit     file is actually the 9,999-th decimal digit and it was rounded-up from a 7 to an 8.    (It would be more helpful if they mentioned doing this!)

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!

The errors 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):

96126 91572 35798 66205 73408 37576 68740 83335 90079 09054 70828 98187

In this next view, the same line appears (without the spaces), but above another corresponding line from a Pi file that has been verified for accuracy:

961269157235798662057340837576687408333590079090547082898187
961269157235798662057340837576687388426640599099350500081337

Assume for the moment, that the second line contains the correct digits. Now copy the underlined  7  and the next seven digits to obtain: 73884266 .   Then click on this link: http://www.angio.net/pi/piquery (which opens a new window) and enter the digits into the search box of Dave Andersen's Pi-Search page. We're going to use the results from his page as a quick, easy and independent check, of our findings. You should now see a page similar to this:

# Results

The string 73884266 was found at position 15093 counting from the first digit
after the decimal point. The 3. is not counted.

Find Next

The string and surrounding digits:

79866205734083757668 73884266 40599099350500081337

This page was brought to you by David G. Andersen [ WWW ] [Email]

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.

## The On-Line Encyclopedia of Integer Sequences

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:

Daniel B. Sedory, The Pi Pages      [a link to this web site -- The Starman]
UCLA Repository, Pi to 100,000 digits, but incorrect after the 15,094-th digit <-- Removed since UCLA server went down!

which used to end with the following statement:

" Warning: There are some erroneous files on the Net that claim to give
large numbers of digits of the decimal expansion of Pi. The error
usually occurs after the 15094-th digit
[that's including the integer 3; it would be one less, or 15,093, if only the decimal digits were being considered -- The Starman].
(w.r.marshall [at] actrix.co.nz), Apr 20, 2001"

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.

__________________
* If you are looking for accurate Pi files on the Net (other than our own), we can only suggest searching various link pages such as the A000796 "Integer Sequences" page mentioned above; and then verifying them of course!

Other Pi files that were correct when checked years ago, but the links are broken now:

[ 1 ] http://www.ccsf.caltech.edu/~roy/upi/pi.50000.html by Roy Williams at Cal Tech, Pasadena, California; independent from my own files, and compiled by someone who knows his numbers.  Although the file contained only 49,980 digits when I checked it, that's more than enough to show it doesn't have the same errors we found in the file above after only 15,093 digits. The digits themselves are bracketed by <PRE> tags, so the file is quite close to being plain text, thus the lines are a fixed length (with UNIX-style returns) composed of 60 digits per line x 833 lines = 49,980 decimal digits.

[ 2 ] http://perso.enst.fr/~pauliat/pi_data_1.html by Christophe Pauliat. Contains exactly 100,000 decimal digits. An HTML page with 50 digits per line separated by a space after each 5 digits. Every block of 1000 digits is separated by 3 blank lines with a label in the left hand margin showing the end of each block and counting by the total number of digits (1000, 2000, 3000, etc.) The digits for this file were computed by Pauliat himself in May of 1994 using a program described here: http://perso.enst.fr/~pauliat/pi_us.html.

3) http://www-stu.pem.cam.ac.uk/~rjw62/maths/pi.html 100,000 decimal digits edited by Robert Whittaker, a Mathematics student at Pembroke College, Cambridge University, England.  HTML page that begins with a .gif of 'Pi = 3.' All the digits are white on a black background, and the number of digits per line depends upon the resolution and/or window-size of your browser! For example, 640x480 gives 60 digits per line, but 800x600 will give 75 dpl. And for those with 1024x768, you'll get an even 100 dpl.

If you're interested in more information on how to do digital comparisons of Pi files, you can use this online reply form to contact me.

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 Math page