Visualize 3D Riemann Sums
Show Riemann sum approximations to the volume under a surface.
plot = Plot3D[Sqrt[1 - x ^ 2 - y ^ 2], {x, -1, 1}, {y, -1, 1}, PlotStyle -> Directive[Opacity[0.5], Yellow], MeshStyle -> LightGray];Grid[Partition[Table[Show[plot, Quiet@DiscretePlot3D[Sqrt[1 - x^2 - y^2], {x, -1, 1, d}, {y, -1, 1, d}, ExtentSize -> Full, FillingStyle -> Opacity[1], PlotStyle -> Lighter[Blue]], Lighting -> "Neutral", ImageSize -> 275, Boxed -> False, PlotRangePadding -> 0, AxesEdge -> {{1, -1}, {-1, -1}, {-1, 1}}], {d, {1, 1 / 2, 1 / 4, 1 / 8}}], 2]]