I want a good dictionary of mathematics/ geometry

Question

I noticed I a made a mistake in some geometrical terminology and wanted to better my life by buying a new dictionary of mathematics or more specialised Geometry. (okay I am just a shopaholic for maths and books)

i went to my local bookshop (and that was one of the biggest bookshops in London UK) but was a bit disapointed by what I could buy, there was only the "Penguin Dictionary of Mathematics" and the "Oxford Dictionary of Mathematics"

I did some tests

First test "polar": (see http://en.wikipedia.org/wiki/Pole_and_polar , this was a term I used in a wrong maner) Penguin does mention it but the description is a bit wonky, only explained for an ellipse and doesn't mention inversion
Oxford doesn't mention polar at all, it goes straight to "polar coordinates"

Second test " stereographic projection " ( see http://en.wikipedia.org/wiki/Stereographic_projection , specially the description or drawing should make sure that you can use this projection for more than a half sphere , and what is the name of the point where the lines start from, "the pole")

Oxford, doesn't give related terminology (no wonder pole was missing anyway) Penguin, bad drawing , looks like only a half spere can be projected.

So at the end I was a disapointed in both of them, can somebody advice a better reference than the two above?

I am specially interested in geometrical terms, and do like figures and construction instructions, my budget is about the price of the two above together, systematic dictionaries (terms related to one object put together) would be even better.

Or maybe even a geometry textbook with a very extensive glossary.

a version for a kindle would also be okay.

Any suggestions for me spending my new year money? (and getting used to use the right terminology)

Answer 1

Honestly, I would get a used textbook college textbook with an extensive glossary. I've always tried to find a good math book in bookstores but they're always pretty weak. A lot of calculus books have good geometry in the first few chapters; even an old edition of Stewart Calculus with all 16 chapters would cover lines, planes, conic sections, polar coordinates, quadric surfaces, etc.

If you like circles a lot, Ken Stephenson's Circle Packing book has good background material on circles on the plane, in spheres, or on the hyperbolic plane.

My last suggestion is a version of Euclid's elements with an index. Much better book than people seem to think; it has a real power in explaining geometric concepts, especially platonic solids.

Answer 2

I have found the "The Universal Encyclopaedia of Mathematics" Pan Reference Books, ISBN 0 330 24396 9, very useful. I have the 1976 paperback edition. It has almost 100 pages of useful formulae. It is very good on geometrical constructions.

However it does fail your two tests "polar" and "stereographic projection". Polar coordinates is described under "coordinate systems".

Answer 3

If you are a shopaholic of good math books, let me recommend you one that has a broad perspective of Math and has projective geometry in it: "Mathematics and Its History" by John Stillwell. I have the third edition (2010), but there are second (2001) and first (1989) editions. I like how the topics are developed in a historic context: interconnected according to its roots throughout civilizations and time.

Answer 4

I've always enjoyed "The Penguin Dictionary of Curious and Interesting Geometry" by David Wells. I'm not sure how easy this is to find in a bookstore or online. High marks also for the Dover books "Advanced Euclidean Geometry" and "College Geometry" , both classics I think. Also, this should be free, Prasalov's Problem book on geometry. Also consider something on Differential Geometry or Algebraic Geometry to get an idea of what you might like to study. Perhaps something like "Geometry and The Imagination" by David Hilbert & Cohn-Vossen, this one is great . Something by H.S.M. Coxeter too , the list of good books is way too long!

Answer 5

I don't know how this is going to sound, but for me the most help "Mathematics Dictionary" is wikipedia.org - It is far from perfect or even complete, and there are a lot of article which are badly written - Still, it is much better than any other Mathematics Dictionary I have ever tried to use.