3

Grapher (sometimes called Grapher.app) is a mathematics graphing application that comes bundled with Mac computers (see https://en.wikipedia.org/wiki/Grapher). I was recently playing around with Grapher, trying to get a feel for it, and discovered some odd behavior.

Suppose you are in 2D mode and you input the equation $|x|=1$. The grapher produces two parallel vertical lines, as expected:

enter image description here

Next, replace the $=$ with an inequality, and you get the region between those two parallel lines (again, nothing out of the ordinary here):

enter image description here

Now let's open a 3D window and again enter the equation $|x|=1$. This time we get two parallel vertical planes, again as expected:

enter image description here

Finally, let's replace the $=$ with an inequality. We ought to get the space between those two planes shaded in. Instead, we get this:

enter image description here

Any idea what's going on?

Blue
  • 75,673
mweiss
  • 23,647
  • 1
    Go to Window -> Show Inspector. Change the Mark to "Box" and the resolution to "High". – Blue Jan 01 '18 at 02:52
  • 2
    Grapher isn't really being very clever---essentially (as far as I can tell), it is sampling points from a grid, then drawing a ball around each point that satisfies the inequality. You can get a slightly better image by selecting the equation you are graphing, then hit the big blue "i" button on the upper-right corner of the window to bring up the inspector. Fiddle with the settings there, then hit the refresh button to see what it does. – Xander Henderson Jan 01 '18 at 02:55
  • @XanderHenderson Got it! The important setting seems to be a popup that lets you choose between "Sphere" and "Box". With the latter, the image looks as it should. If you want to post your response as an answer I'd be happy to upvote and accept it. – mweiss Jan 01 '18 at 02:58
  • Zooming-in and -out shows that @XanderHenderson's interpretation of the sampling procedure appears to be correct. You can also try something like $x^2+y^2+z^2< 10$ at various zoom levels to see sampled approximations of the interior of a sphere. – Blue Jan 01 '18 at 02:59
  • 1
    May I ask why the close vote? If this is not within the scope of the site, what is the math-software tag for? – mweiss Jan 01 '18 at 03:07

0 Answers0