Upper and lower bounds for π based on Vieta’s geometrical approach

Krishna Busawon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 4, Pages 62—72
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Authors and affiliations

Krishna Busawon
Northumbria University
Department of Mathematics, Physics and Electrical Engineering
Faculty of Engineering and Environment
NE1 8ST Newcastle upon Tyne, UK


In this paper, we propose an upper and a lower bound of the number π expressed as the limit to infinity of two sequences. These sequences are constructed using geometric methods based on the Vieta’s approach. As far as geometrical methods for computing π is concerned, numerical results are provided to show that the proposed result is comparable to the existing ones.


  • Pi
  • Vieta’s method
  • Telescopic series

AMS Classification

  • 11B30


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Cite this paper

Busawon, K. (2016). Upper and lower bounds for π based on Vieta’s geometrical approach. Notes on Number Theory and Discrete Mathematics, 22(4), 62-72.

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