# Why does Grapher (a Mac application) plot the 3D inequality $|x|<1$ using spheres? [closed]

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:

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

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

Any idea what's going on?

## closed as off-topic by Xander Henderson, Rohan, Claude Leibovici, Daniel FischerJan 1 '18 at 18:56

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is not about mathematics, within the scope defined in the help center." – Xander Henderson, Rohan, Claude Leibovici, Daniel Fischer
If this question can be reworded to fit the rules in the help center, please edit the question.

• Go to Window -> Show Inspector. Change the Mark to "Box" and the resolution to "High". – Blue Jan 1 '18 at 2:52
• 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 1 '18 at 2:55
• @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 1 '18 at 2:58
• 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 1 '18 at 2:59
• 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 1 '18 at 3:07