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Journal Articles Journal of Formalized Reasoning Year : 2014

Views of Pi: definition and computation

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Abstract

We study several formal proofs and algorithms related to the number π 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 π, 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 π in the proof assistant by relying on rational numbers and decimal representations.

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Dates and versions

hal-01074926 , version 1 (16-10-2014)

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Yves Bertot, Guillaume Allais. Views of Pi: definition and computation. Journal of Formalized Reasoning, 2014, 7 (1), pp.105-129. ⟨10.6092/issn.1972-5787/4343⟩. ⟨hal-01074926⟩
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