How to ensure that all points are fully displayed in a polar coordinate system?

I have a set of coordinates(Table[{n, Sqrt[n]}, {n, 100}]), which I then converted to polar coordinates, and I want to plot them, but the following code doesn't seem to work.

g = CoordinateTransformData["Cartesian" -> "Polar", "Mapping", #] & /@
Table[{n, Sqrt[n]}, {n, 100}];
ListPolarPlot[g, PolarGridLines -> Automatic,
PlotRange -> {{-2, 2}, {-2, 2}}]


Do all points fully display in the polar coordinate system? For example, the last point of g: $$\{ \left.10 \sqrt{101},\tan ^{-1}\left(\frac{1}{10}\right)\right\}$$

How to ensure that all points are fully displayed in a polar coordinate system?

g1 = Map[Reverse, g, {1}];
ListPolarPlot[g1, PolarGridLines -> Automatic, PlotRange -> 200]


• You have to adopt the plot range to the points you want to display. E.g. g[[-1]]={100.499, 0.0996687} Feb 24, 2023 at 8:27
• The structure of data should be ListPolarPlot[{{θ1, r1}, {θ2, r2}, {θ3, r3}}],not ListPolarPlot[{{r1, θ1}, {r2, θ2}, {r3, θ3}}] Feb 24, 2023 at 8:31
• g1 = Reverse[g, {2}] also work. Feb 24, 2023 at 10:02

• According to the document of ListPolarPlot, we need to use ListPolarPlot[{{θ1, r1}, {θ2, r2}, {θ3, r3}}].
• To demenstrate this,here we only plot {10 Sqrt[101], ArcTan[1/10]}.
{θ, r} =
CoordinateTransformData["Cartesian" -> "Polar",
"Mapping", {100, Sqrt[100]}]

ListPolarPlot[{{θ, r}}, PolarGridLines -> Automatic, PlotRange -> .2]


• it's a (+1) from me. good job as always. do you know why it evaluated the wrong structure of the data? seems a bit odd, doesn't it?
– bmf
Feb 24, 2023 at 9:21
• @bmt Thanks! Since the original Cartesian data {n, Sqrt[n]} are on a parabola {x,Sqrt[x]}, the final result should be also a parabola. Feb 24, 2023 at 9:27