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Worse, the calculator is starting to show its age. "Perpendicular lines don't look perpendicular because the window is a rectangle," one Texas-based math teacher told Mic.

...what? If this isn't a misquote, I'm wondering whether it was really a math teacher they talked to.

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It's not a completely unreasonable thing to say, at most it's phrased a bit sloppily. As far as I remember, when you set up the graph there's nothing guiding the user to use limits for the graph that result in a proper 1:1 aspect ratio. Instead if you e.g. want a graph from -3:3 on the X axis, you probably also set up the Y axis as -3:3 too. Since the real screen isn't 1:1, this will result in the graph being squashed down.

And except for the special case of lines that are parallel with the screen edges, a stretched or squashed aspect ratio would indeed distort the angles such that you can't tell which angles are perpendicular and which ones aren't.

In the TI-83, the graph does have several shortcuts you can use to fit the graph, one of them giving you a 1:1 aspect ratio and showing perpendicular lines as actually perpendicular.

The default range for graphs is (-10,10) in both dimensions, while the screen has a 3:2 aspect ratio. The default makes perpendicular lines that aren't on the axes stretched horizontally and appear to be at non right angles.

I think by default it plots from -10 to 10 on both axis. So if you plot y=x and y=-x together they will not look perpendicular on the rectangular screen. You can of course adjust the axes, but if I remember right it's not obvious how to make them match the screen. Graphing tools on a computer or smartphone probably have better default settings.

In the zoom menu there's an option ZSquare (or such) that'll correct the limits to make it fit the aspect ratio.

The must be talking about curved lines that intersect at a perpendicular angle. I think that might make sense.

Actually now that I think about it, two straight lines, one at 45° and one at 135° would display this problem assuming that the display is not displaying the lines at the correct aspect ratio.

I think its possible with perpendicular lines that arent axis-aligned. An m=1 line on a 4:3 aspect ratio will look like an m=0.75 line.

Yeah, that is certainly incorrect. Not only are perpendicular lines perpendicular regardless of the display aspect ratio (edit: as long as you set the projection axes correctly), you can adjust the displayed range in the TI.

And the pixels in the display are square shaped (unlike e.g. Commodore 64 in some modes), so there's no distortion from that either.

I'm not sure what you think the display aspect ratio means, but a 2:1 aspect ratio means that the horizontal axis of a graph will get scaled by a factor of 2 if the window is displaying a square section of space.

The lines y = x and y = -x are perpendicular. 2:1 scaling means the line y = x will appear on screen as y = 0.5x . A line perpendicular to that would have slope -2. But the line y = -x, which is actually perpendicular to y = x, will instead appear on screen as y = -0.5x .

> that the horizontal axis of a graph will get scaled by a factor of 2 if the window is displaying a square section of space.

Yes, exactly. But you can adjust the axes of the graph to get an 1:1 display (ie. x is -10..10 and y is -5..5, not a square space). And that is the default in the TI graphs IIRC.

So as long as you set up the projection to match the screen resolution aspect ratio, you'll get perpendicular lines correctly.

At least on TI-85, I think the pixels are slightly taller than wide, by about 20%. Not square shaped.

I'd assume same is true for other TI-8x calculators.

As discussed in the other comments, the default window is -10..10 and -10..10 in 3:2 aspect ratio.

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