# A parametrization for $\frac{\sin(x)}{x}$ as a revolution surface around $y$ axis

I'm looking for a parametrization for $\frac{\sin(x)}{x}$ as a revolution surface arround the $y$ axis.

I have tried $X(x,y)=\Big(\frac{\sin(y)\sin(x)}{x},x,\frac{\cos(y)\sin(x)}{x}\Big)$.

ParametricPlot3D[
{Sin[y] Sin[x]/x,x ,Cos[y] Sin[x]/x},
{x, 0, 6*Pi}, {y, 0, 2*Pi},
PlotRange -> All
]


But it does not make the surface it should be

Plot3D[Sin[Sqrt[x*x + y*y]]/Sqrt[x*x + y*y], {x, -10, 10}, {y, -10, 10}, PlotRange -> All]


Is my parametrization right? Can you give me some advice? Any help thanks!

Perhaps something like this. Just rotate the original function about the z-axis directly:

RotationMatrix[θ, {0, 0, 1}].{x, 0, Sin[x]/x}
(* {x Cos[θ], x Sin[θ], Sin[x]/x} *)


and so:

ParametricPlot3D[RotationMatrix[θ, {0, 0, 1}].{x, 0, Sin[x]/x}
, {x, 0, 20}, {θ, 0, 2 π}
, RegionFunction -> (-10 <= #1 <= 10 && -10 <= #2 <= 10 &)
, PlotRange -> All
, BoxRatios -> {1, 1, 1/2}] Your original code seems to rotate around the x-axis:

ParametricPlot3D[RotationMatrix[θ, {1, 0, 0}].{x, 0, Sin[x]/x}
, {x, 0, 10}, {θ, 0, 2 π}
, PlotRange -> All
, BoxRatios -> {2, 1, 1}] and rotating it about the y-axis is uninteresting. (Note that I have taken z to be "vertical".)

Try this:

RevolutionPlot3D[Sin[x]/x, {x, 0, 6 \[Pi]}] Have fun!

• Or to rotate around the x-axis: evolutionPlot3D[Sin[x]/x, {x, 0, 6 Pi}, RevolutionAxis -> "X", BoxRatios -> {1, 0.25, 0.25}] – murray Feb 26 '16 at 15:19