By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. The reason this can be expected to work is that the integral can be approximated via Riemann sums. So, the integral is a lower bound for the sum that cannot be more than two off of the actual value.

Accounting for the fact that the integral is nearly mid-way between the sums, the error should less than one, which is why we hit he answer exactly. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How many digits are there in !?

Asked 5 years, 4 months ago. Active 5 years, 4 months ago. Viewed 14k times. How does one calculate the number of digits? To get useful answers please provide some context to your question, including what you tried so far and where you got stuck. Active Oldest Votes. David Peterson David Peterson My answer is similar in that it uses the same sum but then estimates that sum with an integral.

All Digits of My Pi World Record

But, then, I didn't learn Stirling's formula until well after I had learned about Riemann sums. And, as your answer nicely illustrates, it's nice to think about it from a relatively elementary perspective. I think I'll go upvote it! That's actually the best of all the answers! Empy2 Empy2 This is in 64 bit arithmetic in Java. Doing so, I get the same as you. The number of digits will be the number of shifts plus one. Yves Daoust Yves Daoust k 14 14 gold badges 97 97 silver badges bronze badges.Rabinowitz in and investigate by Rabinowitz and Wagon in The algorithm generates the digits sequentially, one at a time, and does not use the digits after they are computed.

Among other sources, the algorithm is described in a very weill written book by Arndt and Haenel. The fundamental idea is that of base conversion. In fact the algorithm for conversion between bases outputs one digit at a time as a true spigot algorithm. Both representations are thought in the form utilized by Horner's method. Rabinowitz has realized, there indeed was such a system albeit an unusual one. The starting point was the series.

However, conversion runs into complications due to the radix not being constant. It may and does happen that the algorithm spews as a decimal digit the number In this case, 1 should be carried to the previous digit and, if the latter is 9, even further left.

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The algorithm accounts for this circumstance. In the applet "Chunk" and "Font size" are output formatting parameters. The applet enforces a limitation of 50, digits - more than a world record some 50 years ago.

Elsewhere there is a faster implementation based on another idea of Rabinowitz and Wagon. Activities Contact Front page Contents Algebra. What is what? This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. What if applet does not run? Related material Read more Expansion of Integers in an Integer Base. Base Binary, Decimal, etc. Implementation of Base Conversion Algorithms.

Conversion of Fractions in Various Bases. Scoring: the simplest of the impartial games. History of the Binary System.Lmod is a tool for sharing modules within a high-performance computing environment e.

We will be loading the Anaconda3 module, which allows us to use many Python libraries that would otherwise be unavailable.

While Anaconda is fine for this tutorial, if you end up using Python for your computational research projects, we strongly recommend using the ACCRE-optimized Python builds on the cluster instead of Anaconda. You can read more here. There are many text editors available for Linux. For new users we recommend nanowhich is simple and easy to use. Other text editors available are vimwhich is more powerful but has a steeper learning curve, and emacswhich is extensible and customizable.

We will use nano for this tutorial, but much documentation on vim and emacs is available online. To start creating the file below with nanotype in nano pi. To close nanopress Control-X or Command-X. You will then be asked if you want to save the file or discard changes.

This is a Python script that calculates the value of pi using the mpmath library, which is included in the Anaconda module. This instructs the scheduler how to run the Python script and what to do with the results. Create a file called pi. Replace your. Type in:. Reference: StackOverflow. Lmod Lmod is a tool for sharing modules within a high-performance computing environment e. Choosing a text editor There are many text editors available for Linux. Writing the Python script Create a file in your home directory called pi.

100000 digits of pi

It only takes a minute to sign up. I saw this question and answer about calculating pi on Stack Overflow, and I decided to write my own program for calculating pi. I used Python and only integers I didn't want to use floating point numbersand used the Gauss—Legendre algorithm because it was the simplest to implement I considered using the Borwein's algorithmbut I didn't want to calculate third roots of numbers, and the Chudnovsky algorithm seemed a little complicated, although maybe I'll give it a try.

My program takes 52 lines of code including commentsand I'm not interested in programs which take too many lines to implement, up to or lines are fine. With 5, digits it took 14 iterations, and with 50, digits 17 iterations, but I didn't count how many iterations it took to calculate the square roots. Is my program efficiently using the Gauss—Legendre algorithmor can it be made more efficient? By the way, add doesn't have to beeven 4 or 5 is enough. But I wanted to make sure all the digits of pi are correct and they are.

I took the square root program from a program I wrote inbut I don't know the name of the algorithm I used and whether it's the most efficient algorithm or not.

Calculate Pi with Python

I prefer not to import modules, but use pure Python either 2 or 3 without any import. And of course if we start with a number closer to the square root such as a or b then it will take fewer iterations to calculate the square root. I think the most efficient method is the Chudnovsky algoritm million digits of Pi, in under 10 minutes! To know the math behind it:. Your comment just repeats the obvious instead say which algorithm you chose and maybe also why you chose that algorithm over another.

This big fat 'top-level' code should be a function, also because Python code runs faster in functions. Mathematical code of this kind really benefits from automated testing, a simple example of automatic testing is:. That's easy to do because each iteration involves a function call.

Simply profile the program by issuing this command from shell:. A report similar to this should appear. It is Newton's method. You could reduce the number of iterations with a better initial guess for the square root instead of 1. Thus either a or b would be a good initial guess for the square root. Using b I see the number of calls go down to Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Pi-calculating program Ask Question.

Asked 5 years, 2 months ago.Pi is not only 3. Get all digits of my pi world record to create music, visualisations, games or scientific publications. All decimal digits are now available in the download section.

If you have no idea what to do with all these digits, have a look at these inspirations. Data sets with more digits are available from archive. In November I made a data set with one trillion decimal digits available for download. The digits are saved as zip-compressed text files in chuncks of one hundred billion digits. Each file has a size of In total you have to download more than Gigabytes. These are the original files from my world record computation in the compressed format of y-cruncher.

You need to compile the DigitViewer provided by A. Yee in order to read these files. Each file contains billion digits and has a size of 78 Gigabytes. The total size is 8. If you encounter permission issues, this could be due to restrictions imposed by your domain administrator. I have verified that the files can be accessed when not being logged in with a google account. As an alternative to the possibly very long download, I can also copy the digits on disks and ship them per mail.

If you need some inspiration about what you could do with all these digits of pi, here are some sites to look at:. Random walk based on pi: pi2e. Krzywinski: mkweb. Pentatonic pi music: www. Normality test of pi: arxiv. My own little game: pi2e.

Why do colliding blocks compute pi?

Home About me Acknowledgements Privacy Contact. Pipi Administrator. Posts by Pipi.Intro to Computer programming worked at calculating digits of pi today. Bailey—Borwein—Plouffe formula. Thanks for the code! Printing is very slow, so you should make it print after the loop.

You can make the while loop eventually end by using a for loop instead. I will subscribe to that writer and his future publications. I see the author has a real knack for this topic. I like that theme, and I am in constant search of new bits and the latest news. I spent only a few minutes reading, and because of well-structured text, I know it completely. Your email address will not be published. Save my name, email, and website in this browser for the next time I comment. Notify me of follow-up comments by email.

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Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I have been thinking about this issue and I can't figure it out. Perhaps you can assist me. The problem is my code isn't working to output digits of pi in the Python coding language.

I know this code can be fixed to work, but I'm not sure what to fix I know how all the code is used to work, but like I said before, I can't get it to shoot out that code. And read about yield operator from here: What does the "yield" keyword do?

If you don't want to implement your own algorithm, you can use mpmath. Update: Code supports older and newer installations of SymPy see comment. The OP's code appears to be based on an implementation of Spigot's algorithm copied from here.

To fix the code per the OP's question although I renamed the variables and functions to match what they were in the original sourceone solution might be:.

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I tested both a few times against this online Pi digit generator. All credit to this Gist by deeplook. Of course you can use diff or tc as well but you'd have to copy these digits from somewhere and there you just submit your program and check whether the score is bigger than From Fabrice Bellard site: Pi Computation algorithm. Sorry for such a straightforward implementation.