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math.MG2026
Focal Sets of the John Ellipsoid of a Simplex from Its Vertices
Anatoly Eydelzon
Starting with the vertices of a simplex in , we build a cubic vector field. If the semiaxes of the simplex's John ellipsoid are distinct, the Jacobian of this field has repea…
math.NT2026
From Pythagorean Runs to Pell-Generated Cubic Runs
Anatoly Eydelzon
A classical Pythagorean run is an identity in which a block of consecutive squares is equal to the immediately following block of consecutive squares. Boardman's construction gives…
math.MG2026
From the Steiner Inellipse to the John Ellipsoid of a Simplex: A Corner-Volume Characterization
Anatoly Eydelzon
For a triangle of area \(T\), a planar corner-area characterization states that an interior point \(M\) lies on the Steiner inellipse precisely when the three corner triangles cut…