Journal of Applied Surface Science(JASS)

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Publications

• Research Article   
  The Bigollφ Method a Pythagorean Unification of Atomic Radius Ratios via the Discriminant Triangle
  Author(s): Thomas A. Husmann*
  
  We present the Bigollφ Method: a single Pythagorean formula that predicts the van der Waals to covalent radius ratio for 97 elements (Z = 3–99) with zero adjustable parameters. The method is derived from the critical Fibonacci Hamiltonian—a 233- site Aubry–André–Harper lattice at self-dual coupling V = 2J with frequency α = 1/φ—whose Cantor spectrum encodes the Py- thagorean triple (√5) 2 + (√8) 2 = (√13) 2. This identity maps directly onto the Dirac energy-momentum relation E2 = p2c2 + m2c4. The resulting universal expression, ratio = √ (1 + (θ(Z) × BOS) 2), collapses seven previously distinct empirical modes into one equation. θ(Z) is constructed from two constants extracted from the .. Read More»
  

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