I've heard that halogen headlights should be replaced in pairs.  I've been wondering if the same is true of HID headlights.  They are much more expensive, so I would like to avoid having to buy two of them if one will suffice.


Question: Around the Clock
Answer: For a constant angular speed watch, if you want some specific figures being placed at the corners, you have to adjust the aspect ratio of the dial rectangle.

A Graphics to begin with:

Manipulate[
    {
                    Dashed, GrayLevel[.7], 
                    InfiniteLine[{0, 0}, Through[{Cos, Sin}[π/6 #]]],
                    Dashing[{}], Black, Thick, 
                    InfiniteLine[{0, 0}, Through[{Cos, Sin}[π/12 + π/6 #]]]
                    } &amp; /@ Range[0, 5] //
        Graphics[{#,
                    EdgeForm[{Black, Thick}], FaceForm[White],
                    Rectangle[##] &amp; @@ (1/
                                2 {{-1, 1}, (Tan[π/6] + ε) {-1, 
                                                1}})
                    },
                PlotRange -&gt; {{-1, 1}, (Tan[π/6] + ε) {-1, 1}},
                Frame -&gt; True, FrameStyle -&gt; Thick, FrameTicks -&gt; None] &amp;,
    {{ε, 0}, -0.5, 10}]




With a proper grid, you can then use the transformation method from other answers to fill in good-looking figures.