A Geometric Analogy for Planck's Radiation Law 1 Based on Effective Spherical Volume

This preprint presents a conceptual geometric analogy for Planck’s radiation law based on an effective spherical volume associated with wavelength. Starting from the frequency form of Planck’s law, the cubic frequency factor is rewritten using the relation λ = c/f, showing that the frequency-domain scaling can be expressed through the reciprocal of a wavelength-defined cubic scale. In this interpretation, each wavelength defines an effective spherical reference volume, while the Planck thermal factor acts as a natural statistical weighting term. The resulting expression is viewed as a product-like structure combining a spherical radiative-energy geometry with a known Planck–Boltzmann type distribution. The work does not attempt to replace the standard quantum derivation of blackbody radiation; rather, it proposes a visual and symbolic framework for connecting wavelength, frequency, effective volume, temperature, and spectral intensity. The manuscript includes analytical reformulation, geometric interpretation, and visual representations showing how normalized Planck intensity may be mapped onto wavelength-defined effective spherical volumes.