Hey guys, here’s a very simple code I wrote, it’s basically just one line. But I don’t understand what is going on at all. I tried to parametrize two functions and to plot the result as a parametric plot. But the plot itself shows 2 lines? Does anyone see what is going on here? Upon changing the lower and upper bounds for u the behavior changes and I’m simply very confused.
Code:
ParametricPlot[{2*u^3/(u^2 - 1), 2*u^3/(1 + u^2)^2}, {u, 1.01, 5},
PlotRange -> All]
Thanks in advance!
J.D.
Janis,
You need to also set the AspectRatio because the plot has a very small y values with huge x values.
ParametricPlot[{2 u^3/(u^2 - 1), 2 u^3/(1 + u^2)^2}, {u, 1.01, 5.},
AspectRatio -> 0.5, PlotRange -> All]
The plot looks like two curves but it is actually the same curve if you look at the data. The manual way to see it is
ListLinePlot[
Table[{2 u^3/(u^2 - 1), 2 u^3/(1 + u^2)^2}, {u, 1.01, 5, .01}],
PlotRange -> All]
Both give you
If you look at the terms, this makes sense:
Plot[{2 u^3/(u^2 - 1), 2 u^3/(1 + u^2)^2}, {u, 1.01, 5}]
The x curve goes to a minimum and then rises again so the parametric plot will have an inflection point.
Regards,
Neil
Thank you, that helps a lot.
J.D.