# Are the plots of these curves correct?

I am working through a set of exercises on parametrised 3D curves. One of these exercises consists of drawing four parametrised curves given in the exercise (in 4 separate plots).

To check my answers I looked at the solutions at the end of the book, but I think they are incorrect. Since the author is a respected mathematician and I am not, I thought I would ask a question here first to confirm my doubts before sending him an email (which I think appropriate, since he keeps a regularly updated list of errata on his website).

The four parametrised curves:

$$a. (t, t^2, t^3), -1 \le t \le 1\\ b. (cos 2\pi t, sin 2\pi t, t), 0 \le t \le 1\\ c. (t, sin 2\pi t, cos 2\pi t), 0 \le t \le 1\\ d. (cos t, sin t, cos t), 0 \le t \le 2\pi$$

And the plots by the author: The text reads "All curves are drawn within a cube with corners at $(\pm 1, \pm 1, \pm 1)$." Although the letters from the exercises aren't repeated here, the first and last one look a lot like my attempts at drawing curves (a) and (d), so I assume it's just a-b-c-d from left to right.

To me the plots given for (a) and (d) look correct, but I think the plots for (b) and (c) are incorrect.
In exercises (b) and (c) the parts of the parametrisation for $z$ and $x$ respectively are equal to $t$ and therefore limited to values in the range $[0, 1]$. Yet, these curves continue past the limits this range imposes, as far as I can tell.

The second (from the left) curve (b) continues from the bottom of the cube to the top, which would imply the $z$ part of the parametrisation is continuous on the interval $[-1, 1]$, which $t$ is not. The same goes for the third (from the left) curve (c), but then with the $x$ parameter.

Please tell me if I overlooked something. Providing correct plots (in case I am right and the plots from the book aren't) would also be much appreciated.

• Jan 13, 2017 at 21:18
• @Martín-BlasPérezPinilla Thanks a lot! I had looked for online plotting software, but those that I found only plotted 2D curves. Jan 13, 2017 at 21:19  