Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

Views of pi : definition and computation

Bertot, Yves and Allais, Guillaume (2014) Views of pi : definition and computation. Journal of Formalized Reasoning, 7 (1). pp. 105-129. ISSN 1972-5787

[img]
Preview
Text (Bertot-Allais-JFR2014-Views-of-PI-definition-and-computation)
Bertot_Allais_JFR2014_Views_of_PI_definition_and_computation.pdf - Final Published Version
License: Creative Commons Attribution 3.0 logo

Download (335kB) | Preview

Abstract

We study several formal proofs and algorithms related to the number pi in the context of Coq's standard library.  In particular, we clarify the relation between roots of the cosine function and the limit of the alternated series whose terms are the inverse of odd natural numbers (known as Leibnitz' formula).We give a formal description of the arctangent function and its expansion as a power series.  We then study other possible descriptions of pi, first as the surface of the unit disk, second as the limit of perimeters of regular polygons with an increasing number of sides.In a third section, we concentrate on techniques to effectively compute approximations of pi in the proof assistant by relying on rational numbers and decimal representations.