# 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.