Pracha Namprasertkul

The Unified Spatial and Harmonic Field: A 3D Tensor Extension of the Golden Ratio, Metallic Means, and the Emergence of Spatial Pitch System

This research paper generalizes and extends the 3D tensor framework established in Namprasertkul (2026) to the broader family of Metallic Means (δ_p) and parallel convergent linear recurrence sequences (such as Lucas sequences and Pell numbers). By executing vector outer products...

The Golden Ratio Family Structure in 2D and 3D Vector Systems

This paper presents an extension of the Golden Ratio (Phi) from a conventional one-dimensional (1D) scalar sequence to two-dimensional (2D) planar and three-dimensional (3D) volumetric tensor fields using vector outer product operations. Conventionally, the Golden Ratio is define...