Skip to main content Accessibility help
×
Home

Irrational Numbers arising from Certain Differential Equations

  • M. Ram Murty (a1) and V. Kumar Murty (a1)

Extract

Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven's proof to show that er is irrational for every non-zero rational r. Dixon [1] made a similar modification to show that π is not algebraic of degree 2. In this note, we prove a general theorem which gives Niven's and Koksma's results as easy corollaries. A suitable modification in our proof also gives Dixon's result.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Irrational Numbers arising from Certain Differential Equations
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Irrational Numbers arising from Certain Differential Equations
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Irrational Numbers arising from Certain Differential Equations
      Available formats
      ×

Copyright

References

Hide All
1. Dixon, J. D., π is not algebraic of degree one or two, Amer. Math. Monthly, 69 (1962), 632.
2. Koksma, J. F., On Niven's proof that π is irrational, Nieuw Archief voor Wiskunde, (2)23 (1949), 39.
3. Niven, I., A simple proof that π is irrational, Bull. Amer. Math. Soc., 53 (1947), 509.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Irrational Numbers arising from Certain Differential Equations

  • M. Ram Murty (a1) and V. Kumar Murty (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.