Message #540

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] higher dimensional book recommendations
Date: Mon, 21 Jul 2008 22:45:56 -0700

I haven’t read Jeffrey Weeks’ book though he did coauthor my favorite
Scientific American article of all time titled "Is Space Finite?"
<http://cosmos.phy.tufts.edu/%7Ezirbel/ast21/sciam/IsSpaceFinite.pdf>
which is related to the work I’ve done cataloguing infinite regular
polyhedra <http://www.superliminal.com/geometry/infinite/infinite.htm>.
Of particular interest to members of our list might be his familiar
games you can play in such tiled spaces
<http://www.geometrygames.org/TorusGames> which includes a nice
implementation of chess in toroidal space. I managed to beat it, but
only because it plays deterministically. If you try that, be sure to
switch from the "fundamental domain" mode to "tiling" mode. We exchanged
a few emails a long time ago and I found him to be a very nice and
approachable guy.

Professor Coxeter <http://en.wikipedia.org/wiki/Coxeter> is most
definitely a giant of mathematics. His book Regular Polytopes
<http://www.amazon.com/exec/obidos/ASIN/0486614808/> is quite possibly
the definitive work on the subject. It’s very dense reading but is a
great reference work to have around if only for the tables of 4D
vertices at the end. I consider it the bible of polyhedra. I was told
that he was a member of a polyhedra mailing list that I was on for
several years along with John Conway
<http://en.wikipedia.org/wiki/John_Horton_Conway>, Mangus Wenninger
<http://en.wikipedia.org/wiki/Magnus_Wenninger> and others. He never
posted there but if he read the list then he probably read some of my posts.

I’m normally much more interested in scientist’s works than I am of the
people themselves but I love a good personal story too and will have to
read Coxeter’s. My favorite so far is The Man Who Loved Only Numbers:
The Story of Paul Erdos and the Search for Mathematical Truth
<http://www.amazon.com/exec/obidos/ASIN/0786884061/qid=997660173/sr=1-1/ref=sc_b_1/107-3481249-3609337>.
A really fun read about an amazing man.

-Melinda

Roice Nelson wrote:
> I’ve finished a couple books recently that I highly enjoyed and are
> apropos to the group.
>
> The Shape of Space
> <http://www.amazon.com/Shape-Space-Pure-Applied-Mathematics/dp/0824707095/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1216142339&sr=8-1>
> by Jeffrey Weeks
>
> This does not require a deep math background - it is described as
> being at a high school level, but I really learned a ton and enjoyed
> it immensely. It is chock-full of dimensional analogy, interesting
> abstractions, and very fun to read with big, easy text and lots of
> pictures! It has also generated a number of thoughts for possible
> additional Rubik analogues in my mind. Briefly describing, the
> flexibility of topology opens up whole new worlds here, and if you
> abstract the original cube as just a 6-cell of faces on a topological
> sphere, all of a sudden there a veritable infinite number of new
> puzzles one could make. I’ve discussed possibly coding with my
> brother a 3D puzzle based on cell divisions of hexagons on a
> topological torus (e.g. a 12-cell is one option we did some sketches
> of; btw, the hexagonal tiling turns out to be important because 3
> cells still meet at each vertex). In the presentation we envision,
> the faces would have to stretch and deform when twisting due to the
> non-uniform curvature of a torus, but we hypercubists definitely don’t
> care about such appearances on our screen ;)
>
> King of Infinite Space: Donald Coxter, the Man Who Saved Geometry
> <http://www.amazon.com/King-Infinite-Space-Coxeter-Geometry/dp/0802714994/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1216142369&sr=1-1>
> by Siobhan Roberts
>
> This is a biography of Donald Coxeter, a new intellectual hero of mine
> after reading it. I really love the genre of mathematical/scientific
> biographies, and this is a good one. The book is much more history
> than math, with plenty of enjoyable anecdotal stories about Coxeter
> and his peers (Hardy, Einstein, Von Neumann, etc.). Overall it is an
> engaging, sweet portrait of someone enthralled with polytopes for his
> entire life.