# On the degree of regularity of a convex polygon

Abstract: We propose a canonical measure for the degree of regularity of a convex polygon.

In an article on this topic [1], a team of three researchers in Barcelona offers criteria that such a measure should meet, and then, like the man who hopped on his horse and galloped off in all directions, offers diverse measures suggested by diverse properties of regular polygons (the properties of being equilateral, equiangular, and of possessing radial symmetry). Moreover, they restrict consideration to polygons having no straight angles.

What we will do herein is obtain a measure of the degree of regularity of a convex polygon that simultaneously takes into account the three cited properties of regular polygons, and that does not need the restriction against straight angles. We do so by generalizing the notion of the apothem, heretofore applicable only to regular polygons, the generalization taking on computational form via averaging via the generalized geometric mean.

On the degree of regularity of a convex polygon

Here it is.
keywords: love

# three equations in three unknowns

Find all points (a, b, c) in R^3 such that:
a(b + c) = 0
b(a + c) = 1
c(a + b) = -3
This problem, in slightly different wording, is on the web, among a set of tournament problems.
Here is the set of tournament problems (as a pdf file).
keywords: Mathematics, Number Theory, challenge

# lorem ipsum

The best way to increase your speed is to bring someone else up to speed.
keywords: karma, teaching, sharing

# wanted software feature

– at least slightly stronger text-processing ability when posting in WordPress – at least the ability to use special symbols such as Greek letters.
keywords: productivity, flexibility

# wanted software feature

– the option, within word-processing, to stay in draft mode, when I put myself in draft mode, until I explicitly opt to exit draft mode. As it is, when I put myself into draft mode, the document comes up in print mode next time I open it. For those, such as myself, who are heavily content-oriented, draft mode is where we want to be almost all the time, and it’s annoying to have to keep switching back to it. (I think this may be yet one more instance, which I have mentioned in a previous blog post (about the position of the END key), of software developers making (sincerely mistaken) poor choices for the users.)
keywords: productivity, flexibility

# lorem ipsum

There are no truly final versions of documents – only pristinely-edited drafts.
(cf: “A work of art is never finished, merely abandoned.” — Leonardo da Vinci)
keywords: perfection, production

# gracefully handling tenant repair calls

Here’s the scoop.
keywords: management, tenants and toilets