Solution and Proof for a Vector Identity and Divergence Problem

Downloadable Files

• Derivation sheet.md
• Illustrations.rar
• Code Snippets.rar
• Animations.rar
• Code Snippets with Diagrams.md

Summary

These files provide a comprehensive visual and conceptual exploration of a theorem describing how specific force fields scale, establishing that their behavior is a direct consequence of classic mathematical rules for proportional functions. This foundation is used to understand how a field spreads outward, revealing that the resulting growth factor is determined by the field's inherent scaling degree and the number of spatial dimensions it occupies. Through interactive tools and animations, these concepts are applied to the physical example of an electric field emanating from a single source point. This application demonstrates a "steepness drop" effect, where a force that typically fades as it moves away is transformed into a field with uniform strength regardless of distance. This transformation reveals a persistent spreading effect throughout space, appearing as a "glow" that perfectly follows the distribution of the local electrical potential.

Kanban

Kanban: ​Homogeneous Flux: The Geometry of Radial Scaling