Yes, this series could be generated by the formula yx! This program generates the polynomial y11/6 x3 - 19/2 x2 50/3 x -8. The first four terms of this polynomial are, in fact, 1, 2, 6,. 11/6 (1)3 - 19/2 (1)2 50/3 -8 11/6 - 19/2 50/3 - 8 ( ) / 6 1 11/6 (2)3 - 19/2 (2)2 50/3 (2) - 8 88 / 6 - 76/2 100/3 - 8 ( ) / 6 2 Etc. Both formulas generate the same set of numbers. Therefore, both are correct solutions to the problem. The fact that you may have come up with the sequence by using the factorial function doesn't make that the "correct answer". There's no way for the computer to know what you were thinking when you typed in the numbers.
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You can use this information to determine whether you need holder to revise the power you guessed or not. Most importantly, when it approaches a constant, the value that it approaches is the constant which is multiplied by the highest power (i.e. F(n n2 (assuming 2 is highest power) if computing this sequence seems to approach 5, then the first term in the function is 5n2). This is a much more efficient algorithm. Computing this way would allow you to compute hundreds of terms instead of just 15 on your site, as long as your server speed was fast enough, which in today's standards, is definitely not a problem. Keep up the good work and enthusiasm! Jay johansen Sep 13, 2011 Hmm, i don't know how you can say that my algorithm "incorrectly maps all functions to polynomials". How can you say that my mapping is incorrect? It derives a polynomial that generates the given set of numbers. Consider the series 1, 2, 6,.
The idea of subtracting numbers in a sequence to obtain the terms has been done many times, however your website does it quite nicely! However, your algorithm is inefficience and I wanted to help you out but giving you a suggestion to improve your solution. If you can "guess" the highest order term, simply by looking at the terms and seeing how each term relates to index. You can guess the highest power this way. Then compute f(n nhighest power. If this value points approaches a constant, you have correctly guessed the highest power. If it approaches 0, the power you have guessed was too high (you should guess again with a lower power and if it approaches infinite the power you guessed was too low (guess again with a higher power).
Off the top of my head I don't know what you could do that would be better, from but, well, there should ions be something. Trial and error would make it very difficult to discover a formula like ysin x / x ln x -. Curtis, sep 12, 2011, i recently view your website regarding your systematic computation of polynomial formulas. One issue i wanted to mention is that it incorrectly maps all functions to polynomials. For example the function n! Which is np and cannot be mapped to a polynomial, but in your website it is mapped to a polynomial in your program. There should be a quick check in place to see if the sequence grows at a rate faster than polynomial speed (i.e. Nk as k- some constant exponent value). Another example.
The version im working on is also designed to calculate it in terms of other mathematical functions (such as sin, mod, log, sqrt, etc). I was wondering if you would be willing to give me a hand with it or any resources i could use for aid. Sep 8, 2011, expanding to other types of equations is an obvious next step. It also seems like a fairly difficult next step. Do you have a plan for how to do it? You could always do it by trial and error,. Have a list of functions and try each in turn until you get something that seems to work.
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Has it out there before you discovered it? Nick, cincinnati, ohio, jay johansen. Jul 29, 2011, i really need to update my page. It turns out that this dante technique was invented by a little-known mathematician named Isaac Newton. I guess if you're going to come in second to someone, isaac Newton isn't a bad person for it. Also, he didn't create a web page to implement. Nick, aug 7, 2011, well, i guess you are in good company.
You should create an algorithm for data analysis. Just tweak the web page code to analyze data for signals (formulas). That awesome technique has to have some commercial/scientific application. I might write some c code for the technique. Chris, sep 6, 2011, i found your site and have found it immensely helpful with a project i have been working on for a while. It is essentially the same formula program you have made, except its designed to analyse multiple columns of data to get the equation, similar to bacon1.
Your method helped me find the formula, which was a 3rd degree polynomial, not fun. Well, i think i have seen this method before. Have you been told any other sources for it? I have taken History of Mathematics. Maybe it was in that class. But your method saved the day - it was the only one that showed up in the search engine.
I was helping a poor College Algebra student who was given the table and asked whether it was proportional. We should have just plotted it to see that it wasn't linear (and/or didn't go through the origin). But I got stubborn and had to find the formula. It was a good exercise. Thank you for posting. Have a nice weekend. Columbus State University, columbus, georgia. Nick, jul 28, 2011, very interesting work. Has anyone ever discussed your method?
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They may be describable by some other sort of formula, a logarithm or trig function or some such. Or they may be just a bunch of random numbers. Azick, feb bill 27, 2011. Sir, i am writing from Cameroon. I write to appreciate your effort of developing a very good program, how to find formula for a set of Numbers. For I have been searching for such a program until this day that I found this t Sir, you limited the program for whole numbers and fractions formula to only 15 at means only the formula for 15 numbers and not more can be obtained. Terry, apr 22, 2011, i googled and found your site tonight for solving a sequence. I had a table with 4 sets of numbers, x and y, with x values starting with 1 and ending with.
to the 9th power. With 15 values, it can go up to x to the 14th power. If the set of numbers you give really requires a polynomial going up to the 14th power, well, i guess it depends what you're doing, but that's a very complicated formula. If, say, you're using numbers from a physics experiment and trying to find a formula to relate them, the odds are that the real formula doesn't go to the 14th power. This program doesn't allow for experimental error, it expects all numbers to be exact. Maybe some day i'll make a version that lets you enter some sort of margin for experimental error. Anyway, my point is, try entering the first 15 numbers from your set and see what formula you get. If it really goes up to the 14th power, you probably have a set of numbers that cannot be described by a polynomial.
a nobody called Isaac Newton has invented this method. Jay johansen, feb 18, 2011, it would be easy eksempel enough to increase the number of input fields on the screen. The logic would be the same. But 15 seems like a very large number. This program finds the simplest polynomial formula that will generate the set of numbers that you give. That is, formulas in the form a b x c x2 dx3. (Where x2 means "x squared x3 means "x cubed etc.
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Comments, fiaz, front dec 3, 2010, thanks for your excellent article. I couldn't really understand why this works. But I could follow through your argument and solve for any future such cases. For your reference, i also happen to see a very concise and sweet method in here. which works nicely and to the point. The method is certainly similar to users, and again I couldn't really understand the theory behind why it works. Thanks regards, fiaz, walter, jan 27, 2011, take a look.