Discussion Overview
The discussion revolves around how to plot a hyperbola parametrically in Mathematica without displaying its asymptotes. Participants explore various methods to achieve this, including the use of exclusions and adjustments to the plotting range.
Discussion Character
- Technical explanation
- Exploratory
- Debate/contested
Main Points Raised
- One participant describes their attempt to plot the hyperbola using the function ParametricPlot[{Sec[t], Tan[t]}, {t, 0, 2 Pi}] and expresses frustration over the appearance of asymptotes.
- Another participant suggests modifying the plot range to avoid asymptotes and provides an alternative plotting method using ParametricPlot[{{Sec[t], Tan[t]}, {Sec[t + Pi], Tan[t + Pi]}}, {t, -Pi/2, Pi/2}].
- A different participant shares a workaround that involves overlaying a plot of the asymptotes in white to visually hide them, although they acknowledge this method is not elegant.
- One participant explains that the asymptotes are a result of the discontinuities in the Sec and Tan functions and suggests using the Exclusions option to avoid them, specifically recommending Exclusions -> {Pi/2, 3 Pi/2}.
Areas of Agreement / Disagreement
Participants express differing views on the best approach to hide asymptotes, with some proposing workarounds while others suggest adjusting the range or using exclusions. No consensus is reached on a definitive solution.
Contextual Notes
Participants note the presence of discontinuities in the functions used, which contribute to the appearance of asymptotes. The discussion includes various methods and suggestions but does not resolve the issue of a straightforward option to disable asymptotes in Mathematica.