Circulation Integral vs. Surface Integral
Downloadable Files
- Derivation sheet.md
- Illustrations.rar
- Code Snippets.rar
- Animations.rar
- Code Snippets with Diagrams.md
- Entity Relations & Quadrant Analysis_Proof 31 of 48.md
Summary
These files explores a fundamental relationship where the movement around a closed loop is directly proportional to the area it encloses. This principle is first demonstrated through interactive simulations where a polygon's boundary gradually matches a perfect circle as more points are added, causing numerical calculations to align with theoretical predictions. The exploration expands to three-dimensional paths that "wiggle" vertically, like a saddle, revealing that these complex curves do not change the final result because their symmetrical ups and downs cancel each other out, leaving only the influence of the path's flat "shadow" on the floor. Finally, the scope moves beyond simple geometry to examine how varying forces interact with curved surfaces, using colourful visual maps to illustrate that the ultimate outcome depends on the unique relationship between the force's local swirl and the surface's specific orientation at every point.
Kanban
Kanban: The Geometry of Stokes: Numerical Verifications and Vector Mechanics
48 Proofs