Calculus in 3D: Tangent Planes & Solids of Revolution

Two of calculus's central ideas, made visible. In "Tangent plane" mode a surface z = f(x, y) hovers above a grid; drag the point across it and watch a translucent plane snap to match the local slope, computed straight from the partial derivatives ∂f/∂x and ∂f/∂y — their combination, the gradient, is drawn as a red arrow pointing the way the surface climbs fastest. In "Solid of revolution" mode a 2D profile curve is spun around an axis and approximated by a stack of disks, each one a term in a Riemann sum; add more, thinner disks and watch the sum converge on the exact definite integral. Switch profiles and point positions freely — every number in the panel is recomputed live from the underlying formulas, not looked up from a table.