       plotting graphs with asymptotes

• To: mathgroup at yoda.physics.unc.edu
• Subject: plotting graphs with asymptotes
• From: p.kent at ic.ac.uk
• Date: Sat, 28 Aug 1993 17:53:35 +0100

```Dear MathGroup,

I'm interested at the moment in plotting simple graphs of the trig
functions as part of a notebook-based tutorial in trig.
So I make a plot of tangent:
Plot[Tan[t],{t,0,2Pi}]
and out comes the graph with spurious lines between - and + infinity
at t=Pi/2 etc. Fair enough---the plotting algorithm is designed for
continuous curves and gets confused by the asymptotes. Then I look in
the "Mathematica Book" for advice on how to deal with asymptotes in
plotting. And on p.134 is a graph of Tan[t] with the spurious lines,
and to my surprise not a mention of how to deal with such situations.
It is similarly neglected in the article on 2D graphics by Nancy
Blachman in the latest Mathematica Journal (vol.3-3).

I've already seen a solution to the problem in Richard Mercer's calcE0
package (free from MathSource, item 0204-691), where his extended
plotting command PlotE0 has a new option called MaxSlope to suppress
lines of very large slope. (The full calcE package is available from
richard at rmercer.wright.edu)

It seems to me that the neglect of asymptotes in Wolfram's main
documentation is a pretty big "hole". Now that more and more students
of high school level are being taught to use Mathematica (and other
systems), and who won't necessarily understand that the spurious lines
in graphs like Tan[t] are actually wrong, this is a hole which needs
some filling.

Does anyone agree with my sentiments?

Phillip Kent
Tranistional Mathematics Project
Imperial College
London.

```

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