       Re: Perpendicular lines do not appear perpendicular

• To: mathgroup at smc.vnet.net
• Subject: [mg100349] Re: [mg100300] Perpendicular lines do not appear perpendicular
• From: John Fultz <jfultz at wolfram.com>
• Date: Mon, 1 Jun 2009 07:11:36 -0400 (EDT)

```One plausible theory is that your monitor doesn't have perfectly square pixels.
In looking up the specs of your monitor, I notice that the resolution is
1680/1050, which would make the aspect ratio of the viewable area of your screen
1.6 if you have perfectly square pixels.  However, the standard aspect ratio of
a wide-screen monitor is, instead, 1.78 (16:9).

I can't tell from the information I can get online, but this raises the natural
question for me...what is the actual aspect ratio of your screen?  Is it a ratio
which preserves square pixels, or the standard 16:9 ratio used for many wide
screen monitors and televisions today?

Mathematica can not tell the difference.  Newer operating systems are starting
include the ability to report more accurate information about monitors.  I'm not
sure off the top of my head if it would be quite so accurate to pick up the
subtle aspect ratio difference I'm suggesting is the problem.  But Mathematica
has a long legacy of working on operating systems which routinely lie...yes,
they really lie...about the actual size of a monitor pixel (including both Mac
and Windows, incidentally...and Linux would just be hopeless in this regard).

The same problem does not exist for printers.  Mathematica, and pretty much
every other software package out there, has supported non-square pixels on
printers forever, since the operating systems gave us the tools to do so easily.

Sincerely,

John Fultz
jfultz at wolfram.com
User Interface Group
Wolfram Research, Inc.

On Sun, 31 May 2009 06:36:06 -0400 (EDT), Bill wrote:
> Perpendicular lines do not appear perpendicular
>
> Hi:
>
> I have taken the line equation 2*x+4*y-6==0, and rotated it 90 degrees
> using a 3x3 rotation matrix.
> Here's the Mathematica 6.0.1 code that I used:
>
> rMat = {{Cos[90 Degree], - Sin[90 Degree], 0}, {Sin[90 Degree],
> Cos[90 Degree], 0}, {0, 0, 1}}
>
> l={2, 4, -6}
>
> rMat.l
>
> Output: {-4,2,-6}
>
> Placing these numbers into the general form of the equation of the line
> Ax+By+c=0, I get -4*x + 2*y - 6 == 0.
> Placing the 2 perpendicular line equations into ContourPlot:
>
> ContourPlot[{2*x + 4*y - 6 == 0, -4*x + 2*y - 6 == 0}, {x, -4,
> 4}, {y, -4, 4}, AspectRatio -> 1]
>
> and plotting, I notice that on my pc screen that the lines do not look
> perpendicular, as does the plot frame.
> Perhaps this is just my computer screen, a HP f2105. I can hold up a
> square cut piece of paper to the lines
> on the screen, and notice the out-of-square condition. I used=
AspectRatio-
> >1, but still no joy.
>
> Question: Can someone suggest a remedy for my problem, if one exists?
>
>
>
> Bill
>
> PS. Mathematica 6.0.1 on a pc with Win XP.

```

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