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It's not a very good one, as it "inflates" the number instead of compresses it.

pi search

Use pi search to find the number. The index into pi is the compressed value.
the 'PPB' algorithm

The PPB algorithm can extract the data without having to calculate pi.

The problem is that with any random or psuedo random sequence, the probability for finding any large amount of data is tiny, and the index would be larger than the actual data.

It inflates the info :(

Consider MathCad. Back when I was doing control theory classes, the interface seemed much more intuitive. You 'wrote' a page of equations, plots, etc. and they were solved automatically. You could even write live reports. It was great for lab and homework writeups. The screenshots don't do it justice. Sadly it is not free, and is windows only.

The parent post almost gives a good link, but there is a gap between the m and l in html. (I've seen this a lot on slashdot. Strange.)
Corrected link.

Today, I have a failed install of MathCAD 2001i. This is a professional tool for people who do math-heavy engineering calculations. It's about as far as you can get from entertainment content. MathSoft made the mistake of using Macrovision copy protection technology. That protection scheme involves creating CD-ROMs that violate the CD-ROM spec, then recognizing them during installation. So it's similar to the "flawed CD" protection scheme for audio CDs. And, sure enough, it doesn't work reliably.

The installation required a reboot of Win2K (a violation of the Windows Logo Program requirements). Then the program complained that I had a debugger installed.

Now that's scary. Macrovision apparently thinks that anybody with development tools (in this case, Microsoft Visual C++ 6.x) is trying to pirate software. The Macrovision program wasn't running under the debugger. The debugger wasn't even running. The debugger was merely installed on the machine.

A call to MathSoft tech support made it clear that this is a known problem. MathSoft suport admits to using Macrovision copy protection, and admits that they've had considerable problems with their protection scheme. They're trying to get Macrovision to fix it, not with much success.

This rather expensive product comes with a 90-day warranty. I told MathSoft support that I want a fix by Monday, or it goes back. I'm also going to try to get Microsoft to pull MathSoft's right to use the "Designed for Windows" logo for nonconformance with the logo standards for nonintrusive, compatible installation.

If you didn't learn in 20 weeks that the FFT is a digital signal processing technique, your class really did suck.

Here's the wavelets URL from the grandparent as a clickable link.

There is a base 10 version of the algorithm available too..

-ShunScene

p.s. Pi has been proven irrational, transcendental and non-algebraic.
However, some posters are assuming that every (finite) number sequence occurs starting at some location in Pi. In chaos terms, this is equivalent to saying there exists a dense orbit in phase space (a sufficient condition for chaos to occur). This has certainly been conjectured, but I have not (yet) seen a proof, and have been led to believe it is independant of claims about the digits of Pi having "normal" auto-correlation co-efficients. (c.f. Polya's constant )

There has existed an algorithm to find the nth hexadecimal digit of PI for a couple of years now. It seems to me, going from hex to binary is trivial.

More info can be found http://www.mathsoft.com/asolve/plouffe/scimath.txt - there.

And does anyone know if that link is incorrect in some way? My DNS can't resolve it.

OK,
- B
--

That's correct, more info here:

http://www.mathsoft.com/asolve/plouffe/plouffe.htm l,

or for goatse.cx aware:

http://www.mathsoft.com/asolve/plouffe/plouffe.htm l

Last I heard, the algorithm only worked in base 16, but that may have changed now.

Unfortunately, pi turns out not to be random. A simple formula can give you any digit of pi that you want. (That page has a link to others which have formulae for other than base 16.)

See a description of some cool formulas for doing so.

A while ago, I got interested in various ways of calculating Pi and saw some of the discoveries made by simon plouffe (this guy memorized the first 5000 places of pi), especially the one he found that allows him to calculate the n-th hexadecimal place of pi without having to get the n-1 places first : this is called digit extraction ,and was kind of unexpected before it was discovered !
There is also a nice little formula from Ramanujan that is an exact sum from 0 to +infinity of Pi
At rank 0, it's got 6 places correct, and it adds 8 correct places each time you increment it (cool eh !)
A couple of Pi links :
Plouffe algorithm
Ramanujan's formula

Original announce of the algorithm

A page with a lot of info/links

Colin Percival pageThe real info about the PiHex project (Probably in the natinal post article too, but I can't access it)

Cheers,

--fred

Original announce of the algorithm

A page with a lot of info/links

Colin Percival pageThe real info about the PiHex project (Probably in the natinal post article too, but I can't access it)

Cheers,

--fred

Going back to who owns the copyright of the individual entries, a lot of entries on the properties of sequences of integers were submitted by Steven Finch of MathSoft. Steven still maintains a website with this material on, so I wonder if CRC will start chasing him? (Maybe he has a separate agreement with CRC, though - I don't know.)

Incidentally, some academic journals in mathematics allow for authors to have an electronic version of their papers on their homepages. The AMS is one example, where you will often see in the copyright notice on a paper `copyright retained by author'. A lot of other journals turn a blind eye. (As you might expect, the copyright notice in the CRC Encyclopedia is the standard `it's ours so hands off' one: no reproducing or transmitting in any form or by any means, electronic or mechanical, etc etc.)

My own feelings are that the best place for the encyclopedia is on the web. Some of the entries are mathematically wrong, and many are misleading. This is not a criticism of Eric, who obviously put a lot of work into the project, it's just a fact that a book containing so much material will contain many many errors. (See the (often extrmely rude) posts from about 5 years ago on sci.math.research complaining about the lack of mathematical precision in the treasure trove!) Having the treasure trove on the web would and should have allowed the project to grow, both in terms of the accuracy and the number of the entries. Sadly, the only way that such errors could be corrected in the printed version would be for CRC to issue a second edition - something I would imagine Eric is now unlikely to want to get involved in...

I'd laugh at your ignorance, but you're not the only one who's gone off about carbon dating in this thread. Carbon dating is only good for measuring ages of organic materials, on earth, and only for a few tens of thousands of years of age.

Go look up Hubble's constant. Here, I'll even do some of your work for you.

Often the Riemann Hypothesis is called Artin's conjecture. Personally I think Riemann's name is overused in mathematical circles. Emil Artin was a much better clavichord player after all...

I'd be interested to see that proof, since a formula for calculating the nth digit of pi does exist. The only catch is, the formula calculates the nth digit of pi in hexadecimal.

If there really is a proof that it's impossible, then presumably that's for base 10 numbers? Do you have a reference?

There is a slightly different perspective that I would like to point out. This would allow more Statistics departments to switch over to Linux. The major (and superior) development environment for Statisticians is S. A Linux port for S already exist. More importantly there is R, a free implementation of S which is equally good if not better than the commercial version. So, now you have essentially everything you need as a statistician on Linux.

Nope, not joking. Goedel also had a Completeness Theorem, which states what the original poster says it does -- that first-order predicate logic is complete. However, I disagree with the poster that you can construct FLT as a sentence of first-order predicate calculus, because I don't think you can get the operation of power, among others, out of FOPC. Therefore, FLT is a sentence of elementary number theory which is not a sentence of FOPC, and is therefore, in principle, the sort of thing which might be unprovable.

To prove I'm not smoking crack, I'll note that there are Diophantine representations of FLT and that Greg Chaitin has shown that there are Diophantine equations which are unprovable in Goedel's sense. FLT is clearly not one of them, but Turing's work shows us that we can't actually prove unprovability about a given theorem. So, FLT might have been unprovable.

BTW, it's difficult to give old KG his umlaut, but at least leave him the dignity of an 'e' after the 'o'. Otherwise the English speaking world will start pronouncing him as "Go - dell", which is already beginning to become a problem.

about human eye -
- most wavelet transform based compression algorythms achieve a better quality due to the fact, that it naturally concentrates on changes - edges - of the image - the same thing human eye and mind concentrates on.
Look at some papers on image processing...
Notice one about deblocking of JPEG compressed images, for example...

Wavelet based techniques are much better - less artifacts (no blockiness and other crap), smaller.
But - most of algorythms are proprietory ;(

BTW. The example in the post above - with a faint line - is exactly where DWT based techniques shine - they preserve singularity type structure in the data. Look up publications on wavelet denoising.

Good start page