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The Siebeck-Marden-Northshield Theorem and the Real Roots of the Symbolic Cubic Equation

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arxiv 2107.01847 v2 pith:YFUIE7P4 submitted 2021-07-05 math.GM

classification math.GM
keywords polynomialcubicrealrootsontoprojectssiebeck-marden-northshieldsymbolic
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abstract

The isolation intervals of the real roots of the symbolic monic cubic polynomial $x^3 + a x^2 + b x + c$ are determined, in terms of the coefficients of the polynomial, by solving the Siebeck-Marden-Northshield triangle - the equilateral triangle that projects onto the three real roots of the cubic polynomial and whose inscribed circle projects onto an interval with endpoints equal to stationary points of the polynomial

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Three-layer water flows: Dirichlet-Neumann operators and approximations

    physics.flu-dyn 2026-08 conditional novelty 5.0 of 10

    Three-layer stratified water flows are cast in Hamiltonian form using Dirichlet-Neumann operators, yielding a dispersion relation and approximate wave speed formulas.

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