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I've answered a question on the intuition behind the Arc Length formula.

I would really like to add a couple of simple pictures to illustrate the two distance computations. They would involve a simple curved line, a straight line, and some labels.

Locally (i.e., at my laptop at home), the best I can do is use Paint, and I'm very unhappy with the results. Alternatively, I can produce pictures using LaTeX's picture environment (I'm reasonably good at it) and then create PDFs out of them, but they tend to be page-sized, which is overkill here.

I know I've seen several people illustrate their responses with small simple graphs, and if someone could point me in the right direction I would appreciate it.

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  • $\begingroup$ Why not simply sketch them by hand (and scan them)? That's worked well for centuries. $\endgroup$
    – Bill Dubuque
    Commented Mar 19, 2011 at 22:24
  • $\begingroup$ Is Paint the one in Windows? $\endgroup$
    – Tim
    Commented Mar 19, 2011 at 22:30
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    $\begingroup$ I've seen some recommendations for the free program GeoGebra though I've never had the chance to try it. $\endgroup$
    – Bill Dubuque
    Commented Mar 19, 2011 at 22:41
  • $\begingroup$ @Tim Yes, it is. $\endgroup$
    – Arturo Magidin
    Commented Mar 19, 2011 at 22:43
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    $\begingroup$ @Bill: Because scanning is annoyingly difficult in my set-up. $\endgroup$
    – Arturo Magidin
    Commented Mar 19, 2011 at 22:43
  • $\begingroup$ See also: Creating diagrams. $\endgroup$
    – Martin Sleziak
    Commented Oct 3, 2017 at 8:05

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For WYGIWYS editors, I have tried

For Latex, you can also try TIkz/PGF.

Also there is graphviz

This link is also helpful: Online tool for making graphs (vertices and edges)?

Added:

Probably this list will meet your need:

Interactive geometry software (IGS, or dynamic geometry environments, DGEs) are computer programs which allow one to create and then manipulate geometric constructions.

As Bill Dubuque said, GeoGebra is a good one. You can also test others in the list.

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  • $\begingroup$ Thanks. I used GeoGebra; other than not being able to figure out how to put labels on a few points, it worked pretty well. $\endgroup$
    – Arturo Magidin
    Commented Mar 20, 2011 at 4:32
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Since you're reasonable good at doing it in LaTeX, you'll be interested in the standalone class. It's purpose is just what you want: Produce an image file that is as small as possible. Have a look at the following two questions over at tex.sx for how to use it:

  1. Compile a latex document into a png image that's as short as possible.

  2. TikZ to non-PDF.

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  • $\begingroup$ That looks pretty good. Thanks! $\endgroup$
    – Arturo Magidin
    Commented Mar 20, 2011 at 20:19
  • $\begingroup$ @Arturo: I'd like to emphatically endorse this method. We've been using it over at the TeX-SX site and the workflow is really, really easy. $\endgroup$
    – Andrew Stacey
    Commented Mar 25, 2011 at 8:53
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I tend to use one of three programs—Mathematica, Adobe Illustrator, or Geometer's Sketchpad—but since all three are commercial, that may not be what you want.

Since you said you can probably produce PDFs of what you want, just not in a suitable size, your best bet may be to look for ways to resize and convert those PDFs to PNGs (or some other suitable graphics format). Mac OS X's Preview.app can do this very nicely. I think you can do it with Acrobat Pro, but that's back to commercial software. Maybe GIMP or some other image-editing/manipulation software.

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I used to have your problem.

What I often do is take diagrams from $\LaTeX$, GeoGebra, R, Excel or whatever, copy them (and if that does not work, then use the Prt Scrn button), then paste into Paint, remove what I don't want, and save as a .png file.

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There's also the Google Charts API

http://code.google.com/apis/chart/

Though I'm not sure this is exactly suitable to math-specific needs, it's pretty good at a wide variety of things.

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