How do you calculate pi... ...from SCRATCH?

Jump to Last Post 1-3 of 3 discussions (4 posts)
  1. stanwshura profile image71
    stanwshuraposted 11 years ago

    How do you calculate pi... ...from SCRATCH?

    Does there exist an algebraic or arithmatic means, completely devoid of any need for graphical or trigonometric methodologies, and, you just might guess, similarly requiring no prior understanding of integrals or derivatives, such that you can produce a fraction/ratio by means of some formulaic procedure that, applied over and over, ad infinitum, which, by infinite application thereof results in a quotient that is "equal to" pi in that the more such operation is applied/calculated (longhand) the more infinitely accurate it is in answering C/D?

  2. profile image0
    calculus-geometryposted 11 years ago

    There are Monte-Carlo methods for calculating pi that require nothing but iterating a certain procedure, recording the ratio or successes to total attempts, and then using some algebraic formula to convert that ratio to pi.

    See this user's articles for a humorous take on calculating pi with such techniques:

    http://bubba-math.hubpages.com/hub/How- … le-Problem

    There are also infinite series and infinite products that converge to algebraic functions of pi. For example, the alternating series

    1 - 1/3 + 1/5  - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 ...

    converges to pi/4. Here is a mathworld reference for similar pi formulas

    http://mathworld.wolfram.com/PiFormulas.html

  3. Nateerrr profile image60
    Nateerrrposted 11 years ago

    You could always do what the ancient Babylonians did, which sufficed for centuries:
    1) Get some circular objects and measure their diameter
    2) Measure those same objects' circumference (which can be tricky!)
    3) Compare the two measurements for each circle and observe that they are about 3 (a tad bit more than 3, to be precise) times bigger around than they are across, which seems to happen for every circle, all the time
    And there you have the essence of pi! Nowadays with our fancy mathematics and computing machines, we have far more information about pi and all its infinite decimals, but back in the day, "about 3" was good enough.

    1. stanwshura profile image71
      stanwshuraposted 11 years agoin reply to this

      Thanks for the reminder of the seeds of concrete and manipulable numeracy, and the great thinkers and how they started.  I am, however, ahem...infinitely more interested in the formulae and mathematics used to refine it to its nonexistant end!  smile

 
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://corp.maven.io/privacy-policy

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)
ClickscoThis is a data management platform studying reader behavior (Privacy Policy)