Parametric plot radial Colouring

Question

I would like to draw a circular segment with a colour gradient based on the radial distance from the center. Currently I have:

ParametricPlot[
    {ρ Cos[θ], ρ Sin[θ]}, {ρ, 5, 25}, {θ, π/4, (3 π)/4},
    ColorFunction -> Function[{x, y}, Hue[Sqrt[x^2 + y^2]]],
    Axes -> False, Frame -> False
]

which gives the following:

Which clearly is not coloured according to the radial distance from the centre. How can I do this?

Answer 1

The problem you're encountering is due to ColorFunctionScaling->True. Set it to False, and then normalize your Hue function:

ParametricPlot[
    {ρ Cos[θ], ρ Sin[θ]},
    {ρ, 5, 25},
    {θ, π/4, 3 π/4},
    ColorFunction->Function[{x,y},Hue[Sqrt[x^2+y^2]/25]],
    ColorFunctionScaling->False,
    Axes->False,
    Frame->False
]