2026/06/24 by Arjen Toni Dijksman · 1 voice
Mathematics · Physics and Astronomy · #math.MG #math-ph
We present the ''Power Spiral Map'', a continuous angular evolution of the linear coordinate grid established in our previous work. While that previous Power Map utilized a seed value translating along a horizontal axis, this work builds upon a seed angle (θ) projected onto a unit diameter circle. This operation controls two coupled geometric behaviors: an internal area-preserving partition of unity within a reference square (cos 2 θ + sin 2 θ = 1) and an external recursive scaling mechanism (sec θ and cos θ) that dictates the expansion or contraction of successive generations of squares unfolding as a spiral in the 2D plane. We demonstrate that continuous variation of this angular parameter generates discrete geometric alignments that yield polynomial identities, with examples of the Golden Ratio (Φ) and the Plastic Ratio (ψ) defined through purely planar intersections.