Published July 22, 2026 | Version v1.0.2
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A Constructive N-Series Acceleration Law for Polygonal Approximation of π

Authors/Creators

Description

This paper applies structured asymptotic cancellation to accelerate polygonal approximations of π via an N-series operator, using a π-free Richardson-type acceleration scheme. This is the third paper in a three-part research sequence on constructible approximation and cubic-order error refinement.

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nseries_pi_acceleration.pdf

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Additional details

Identifiers

URL
https://github.com/CWBaker360/N-Series-pi-acceleration

Related works

Is supplement to
Preprint: https://github.com/CWBaker360/Constructible-Cubic-Trisection (URL)
Preprint: https://github.com/CWBaker360/proportional-subtended-cubic-refinement (URL)

Dates

Submitted
2026-07-22
A Constructive N-Series Acceleration Law for Polygonal Approximation of π

Software

Repository URL
https://github.com/CWBaker360/N-Series-pi-acceleration
Programming language
Python , Python console
Development Status
Active

References

  • Archimedes, Measurement of a Circle, in The Works of Archimedes, edited by T. L. Heath, Cambridge University Press, Cambridge, 1897
  • L. F. Richardson, "The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam," Philosophical Transactions of the Royal Society of London. Series A, 210 (1911), 307–357
  • J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed., Texts in Applied Mathematics, vol. 12, Springer, New York, 2002.
  • W. Baker, A Constructive Cubic Error Cascade for Approximate Angle Trisection, working manuscript, 2026.