allonymy

A notice to renew my domain registration prompts thoughts of what I might have used instead: *ansher, anwood, tonsher, tonwood* ?

*tonsher* reminds me of an acquaintance whose bald spot looks uncannily like a monk’s tonsure — and that’s even funnier on a Jew. My own bald spot is not so sharply defined.

elusive avoidance

I’ve been designing printable models of the Lawson-Klein surface

w = cos(u) cos(2v)

x = cos(u) sin(2v)

y = sin(u) cos(v)

z = sin(u) sin(v)
As you can plainly see, this figure lives in S3 (positively curved 3-space), so stereographic projection can bring it into E3 (Euclidean 3-space) without adding more self-intersections. (It crosses itself at u=nπ.)

To minimize the distortion of the projection, I want the projection center to be as far as possible from the surface. One thing I tried was pursuit: starting with an arbitrary point P in S3 and an arbitrary point L(u,v) in the surface, move (u,v) to bring L closer to P while simultaneously moving P away from L. This gets me nowhere so far: either it fails to converge or P converges to the antipodes of L, which is also in the surface (change u by π).

hidden dragon

For years I’ve occasionally had a mysterious itch at my lowest left rib, nothing showing on the skin. Now it has spread rightward at the same altitude, making me think: could this be mild shingles?

unapologetically one-sided

My newest design on Shapeways is a model of the Lawson-Klein surface : a stereographic projection of

( cos(u)cos(2v), cos(u)sin(2v), sin(u)cos(v), sin(u)sin(v) )

oddly tempting

I hadn’t noticed before that my webhost offers MediaWiki. Some of the things I write here are not news, really, but things that sorta belong in my permanent exhibition but are too wordy for that page.

I’ll think about that.

models of the 35 smallest fullerenes

I noticed that Shapeways had 13 models of the roundest of the fullerenes (one of the 1812 forms of C60), but none of the less regular forms; so I made some.

Each of the white pieces has mirror symmetry; the red pieces are chiral. Not shown (because it hasn’t been printed yet): the blue set, which is a reflection of the red set. The idea is that you buy both red and blue if and only if you count reflected chiral forms separately.

These figures have 12 pentagons and up to 8 hexagons. They include the two smallest forms with no nontrivial symmetries, and the two smallest with no ‘peaks’ where three pentagons meet.