Bhāradvāja Vimāna: The Axis of Convergence
Year: 2026
Type: preprint
Abstract: In this paper, I construct a single continuous structure strictly and simultaneously generalizing: Gauss’s AGM, Landen transformations, Borwein algorithms, Newton and Halley iteration, Chebyshev polynomials, de Moivre’s theorem, and Brahmagupta’s bhāvanā. The construction is the p-th power of the mūla-bheda coordinate introduced in my first paper: μ ↦ μᵖ. Its convergence law is exact, Dₙ = pⁿD₀, and the maps compose, Vₚ ∘ Vᵣ = Vₚᵣ. Thus the order of convergence is the group parameter itself. The axis is polynomial at integer p, algebraic at rational p, and transcendental otherwise. For π, the algebraically constructible orders are exactly ℚ. The classical integer-order algorithms are particular points on this axis; rational orders between them are constructible as well.
Author: Bhardwaj, Ram
Institution: Indian Institute of Technology Madras
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203954373
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