# Message #539

From: Roice Nelson <roice3@gmail.com>

Subject: higher dimensional book recommendations

Date: Mon, 21 Jul 2008 18:14:11 -0500

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.

Hope this finds you all well,

Roice