I‘ve been looking for a euclidean geometry book filled with as many theorems and axioms as possible, even better if it‘s as condensed as possible (say, proofs given separately in another book, or not at all, doesn‘t matter. In short, no proving, just the facts).
I do realize that I‘m not being entirely descriptive of my intentions of use for this book, so let‘s say I‘m looking at an IMO-level book - actually more like last-minute-speed-revision/cramming (geometry‘s not exactly my strong suit, the rest is fine)
Requirements be damned now if they are too demanding (I‘d like to think so), all book recommendations are welcome and are free to ignore as many of my requirements, except for one - it should be really, really short (just the lemmas, that is)
Thanks!
P.S. I got three months; I guess you can follow from that ;)
Euclid is said to have replied to King Ptolemy's request for an easier way of learning mathematics that “there is no Royal Road to geometry”. The list of Euclidean geometry propositions is long. In fact, it should be infinite and therefore unlearnable by a finite mind (that is why we should believe in The Book. :-) A part of N.V. Efimov’s book devoted to basics of Euclidean geometry with accurate proofs from axioms contains about 250 pages. Thus, the geometry scope to be learned is very restricted by our time and mental possibilities. For instance, for me, because geometry is not my strong suit too and three months is a tiny piece of time for IMO preparation. So I think that the aim of the learning should be formulated wisely, and it determines its form. The plain lists can be found in reference books or mathematical encyclopedias. But it seems that in order to obtain an effective toolbox for a mathematical olympiad you should read more specialized books. I know places where such Russian books can be found (for instance, here) and your may search English translations. Especially I remember different problem books of geometry, plane geometry, solid geometry by V.V. Prasolov and/or I.F. Sharygin. A translation of the first volume of one of these books is here.