I just created the following image of a pentagram for Wikipedia:

Non-Desargues configuration: pentagram inscribed in another pentagram forming ten lines crossing in triples at ten points

It's a projective configuration that has the same number of points, lines, and incidences as the Desargues configuration, but is not equivalent to it. Michael Hardy found its description in an old forum posting.

If you look at the source code I used to draw it, you'll see that it uses neusis, or the modern equivalent, binary search, to find the appropriate scale of the outside pentagram relative to the inside one so that the points all line up. (You'll also see that I don't comment heavily when I write quick one-off code like this, but I hope it's short enough to be readable anyway.) Is this figure drawable with compass and unmarked straightedge alone?

(Hint: what kind of function is the binary search finding the root of?)




Comments:

zsmith721: interesting
2008-04-13T06:24:13Z
Sweet. Kinda random. All kinds of interesting analyses can be done on reference sites like Wikipedia. Personally, I also like to check out About.com and Site605 (http://www.site605.com) - there are a few other reference sites that I think will give Wikipedia a run for their money.
yodha:
2008-04-15T03:26:37Z
I'm curious, what software do you use to generate your diagrams for these journal posts?
11011110:
2008-04-15T03:29:12Z
Usually Adobe Illustrator (and I did use Illustrator to generate the png format for this one) but in this case it was primarily a custom Python program, using the pyx package to generate the graphics. You can see the program itself by following the source link in the post.
yodha:
2008-04-15T03:44:36Z
Will check it out, thanks!