1. I was in the middle of an important study, when I came apon a problem. I cannot figure out a way to find the root that represents a specific irrational number exact to the 10^600th decimal space. If you have any Ideas, you might have a hand in creating a better world for us all.  2.

3. Sorry. You lost me round about the part where you got to problem. If you can't hit it with a hammer, or cook it in a micro-wave, then I don't know what to do with it.
Don't despair, there are some mathematically inclined members, who can hopefully contribute.  4. Need clarification.

Do you mean finding a general polynomial with a root that matches an apparently irrational number given to 600 significant digits? Or are you restricting yourself to roots of polynomials of the form x^n = a, so that the nth root of a matches your 600 digits?

I have never heard of mathematics like this because I don't know that there has ever been a need. Generally if you have an irrational number then you have a method to generate that number which means you basically already have the equivalent of a polynomial with a root that matches that number.

I think you need to make more conditions on the polynomial you want for I think there are rather trivial answers to your question. For example,

Take your 600 digit number and square it. For anything that looks like an irrational number the exact answer to squaring it should have near 1200 digits. If you trucate the result to something less than 1200 digits but more that 600 digits then the square root of the result should match your starting number to the first 600 digits and is most likely to be irrational as well.

For example take the square root of 2 to 6 digits: 1.41421
The square of this to 10 digits is 1.999989924
If we round this off to 6 digits we get 1.99999
the square root of 1.99999 to 10 digits is 1.414210027
this matches our starting number to the first 6 digits and it is probably irrational so did I not find a root matching an irrational number given to 6 digits?

I doubt that this is what you are looking for. I am giving it as an example so you can explain why this is not what you need and therefore explain further criterion which must be met!  5. I have an extremely long number. it is in reality, 118,565 digets long. I would like to write it in a more simple manner. I have found that putting it at the begining of the decimal in an irrational number and than finding the root that would equal an irrational decimal that started with my number (if that makes any sence) could be a very effective way of transporting this number on nothing but a piece of paper. My limited mathematical skills restrict me from finding this, "4th root of 6" that would result in a irrational number that starts with my exact 118,565 digets.

I realize that there are a limited amount of irrational numbers that could be found in a simple "2nd root of 3". For this reason, I did infact create a formula that would pull around 7.6953647*10^34 irrational numbers (wich might not be enough to chose from). I do not know how to come up with the "equation" that would yield my number.

My equation was basicly a bunch of roots in a fraction, multiplied and divided by eachother with some restrictions to the numbers that could be inserted as the index and radicand. the radicand, for example could not be written as a fraction with mor than 4 digets in the numerator, and 5 digets in the dennominator, though it can if you want have less. Yes, it sounds to simple, but...simple is good, right?

I hope I was clear enough this time. If you want though, I could clarify it to a greater extent.  6. I was afraid it was something like this, because it is impossible for many reasons. Simple information theory for one thing, you cannot represent a large quantity of general information accurately with less information. Now if you only need 95% accuracy there might be something you can do with a fourier analysis (for example). The whole point is that in general, the information received is always less than or equal to the the information transmitted. Some types of information have patterns you take advantage of, like english text and so zip file copmression can take advantage of this to compress such text files into really small sizes. But your many digit number does not sound like it is going to have any patterns to take advantage of, so you cannot do better than a binary representation of the number (an ascii text representation is of course much less efficient).

Most numbers are irrational. Pick a real number at random and that probability that it is not irrational is zero. This is in fact one reason why I could say that the roots generated by the process I gave before are probably irrational (though the real reason is rarity of perfect squares). If you consider all the irrational numbers that can be generated using only 10 rational numbers, by some fixed process this is an insignificant portion of the entire set of irrational numbers. This is not entirely applicable to your problem because you don't need to generate one particular irrational number but one of infinitely many that match the first 118,565 digits (and this is a significant portion of the entire set of irrational numbers, by the way).

I am sure you can make a function to reproduce your number but not with less information. In fact, it will most definitely require more information to accurately reproduce the original. For example, if the message length varies then you also need to send the information on where to truncate the irrational number in order to get the original number.  Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement