Re: DiscretePlot

• To: mathgroup at smc.vnet.net
• Subject: [mg96773] Re: [mg96697] DiscretePlot
• From: peter <plindsay.0 at gmail.com>
• Date: Tue, 24 Feb 2009 05:47:46 -0500 (EST)
• References: <200902220038.TAA08394@smc.vnet.net>

```well, I'm sure its all explained in the manual....

2009/2/22 Helen Read <hpr at together.net>:
> I recently started the chapter on series in my Calculus II classes. I
> like to have my students make tables and plots of terms and partial sums
> of series, to help them develop some intuition about what it means for a
> series to converge or diverge, which leads naturally into convergence
> tests. (Give them something where it's hard to determine
> convergence/divergence from tables and plots, and the students will
> *ask* how can we know for sure.) Prior to Mathematica 7, we always had
> to start with a table, name it something, and use ListPlot to plot it.
> So now with Mathematica 7, I still have my students make some smallish
> tables (I like them to have numbers to look at it in addition to plots),
> but now we can plot directly with the new DiscretePlot. I like
> DiscretePlot a lot, except for one complaint I will get to below.
>
> As an example, consider the alternating harmonic series. My students
> know how to define a function for the terms and a function to generate
> the partial sums, then plot the terms or the partial sums with
> DiscretePlot, like so.
>
> a[n_] = (-1)^(n + 1)/n
>
> s[k_] := Sum[a[n], {n, 1, k}]
>
> DiscretePlot[s[k], {k, 1, 100},PlotLabel->"Partial sums"]
>
> We can turn off the filling. (I like the filling sometimes, but not always.)
>
> DiscretePlot[s[k], {k, 1, 100}, Filling -> None]
>
> All well and good.
>
> However, unlike ListPlot (which has Joined->False by default),
> DiscretePlot has Joined->Automatic by default. If we plot greater than
> 149 points with DiscretePlot, Mathematica joins the points, and it's a
> royal mess.
>
> DiscretePlot[s[k], {k, 1, 149}, Filling -> None]  (* this is fine *)
>
>
> DiscretePlot[s[k], {k, 1, 150}, Filling -> None]  (* this is a wreck *)
>
> As another example, try using DiscretePlot to plot terms of the sequence
> b(n)=sin(n).
>
> b[n_] = Sin[n];
> DiscretePlot[b[n], {n, 0, 500}, Filling -> None]
>
> Well that's just hideous. Students just learning about sequences and
> series aren't going to have any idea what's going on.
>
> We can fix this behavior by setting Joined->False, like this:
>
> DiscretePlot[s[k], {k, 1, 150}, Filling -> None, Joined -> False]
>
> DiscretePlot[b[n], {n, 0, 500}, Filling -> None, Joined -> False]
>
> The students are having trouble remembering to do this, though, and I
> wonder why on earth Wolfram would design DiscretePlot this way. When I
> go to make a DiscretePlot, I do not *ever* expect -- or want -- the
> points to be joined. And why are the points not joined for < 150 points,
> and joined for >= 150 points? This seems completely arbitrary, and in
> fact I only discovered the 150 point cut-off by trial and error, and
> could find no explanation in the Documention as to what
> Joined->Automatic even does.
>
> I'd be far happier if DiscretePlot had Joined->False by default.
>
> --