ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Approximate pi in Java

Updated on May 5, 2011

Introduction

This code illustrates a simple iterative method for approximating the value of pi. As we all know, pi represents the ratio of a circle's circumference to it's diameter. The number does not change, regardless of the size of the circle. Big circles and little circles all share the same value of π.

Pi is an irrational number. In other words, people that use π in their equations tend to be easily upset by seemingly insignificant issues. Mathematicians can be a touchy bunch and for that reason are not invited to many casual parties. Perhaps this is why they have their own conventions and university departments.

How does it work?

It works perfectly. As long as the floating point data items are not permitted to overflow, it works.

The floating point division in lines 22 and 23 are a weak point. As we all know, the float data type in Java supports about 6.5 digits, therefore we observe that floating point error begins to creep into the calculations rather quickly.

Future Work

Ambitious programmers and bored readers may wish to improve upon the algorithm by implementing a data type that resists precision loss with greater efficacy. Converting the calculations to use the double data type presents little challenge, but would improve resolution relatively significantly.

Another challenge might be to rewrite all calculations with the BigInteger class provided by Java. Throughput would drastically decrease, but precision would take a major leap forward.

// This method approximates pi through an interative calculation.
// It prints the result to stdout rather than return it.
// The calculation stops when a number between 3.14160 and 4.14159 is reached.
// This method could be easily enhanced by narrowing the range.
// A narrower range would yield a closer approximation of pi.
// Happy pi day!


public static void approxpi()         // Approximate pi
{
    double x =1;
    double y =3;
    int pass =0;
    double pi1 = 0;
    double pi2 = 0;

//    while (Math.abs(3.14160 -pi2)> .00001)
    while (!(pi2 <= 3.14160 && pi2 >= 3.14159))
    {
        pass=pass+1;
        pi1 = (4./x) - (4./y);    //given equation
        x=x+4;
        y=y+4;
        pi2 = pi2 +pi1;
    }
    System.out.print("\n\nValue of pi is approx.: "+pi2+", terms needed ="+pass);
}

Comments

    0 of 8192 characters used
    Post Comment

    • profile image

      banania 

      6 years ago

      c nul

    • seedling profile image

      seedling 

      7 years ago

      You might need to reformat the article since the code is disappearing under an advertisement.

    • profile image

      Saafir 

      8 years ago

      Thanks for the code

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)