# [Reading] ➸ Introduction to Geometry By Richard Rusczyk – Dolove.info

Introduction To Geometry SkillsYouNeed Geometry Comes From The Greek Meaning Earth Measurement And Is The Visual Study Of Shapes, Sizes And Patterns, And How They Fit Together In Space You Will Find That Our Geometry Pages Contain Lots Of Diagrams To Help You Understand The SubjectIntroduction To Geometry COXETER, HSMNotRetrouvez Introduction To Geometry Et Des Millions De Livres En Stock SurAchetez Neuf Ou D OccasionIntroduction To Geometry Rusczyk, RichardNotRetrouvez Introduction To Geometry Et Des Millions De Livres En Stock SurAchetez Neuf Ou D OccasionIntroduction To Geometry McFarland, LydiaNotRetrouvez Introduction To Geometry Et Des Millions De Livres En Stock SurAchetez Neuf Ou D OccasionIntroduction To Geometry E P S M CoxeterHowever Geometry For The Boomer Generation Has Been Easier To Learn Because Of The Classic HSM Coxeter Introduction To Geometry Thisfinal Edition Simply Perfects Thefirst Edition That Helped Me Start My Career In Computer Graphics The Minor Typographical Errors Have Been Fixed One Such Defect In The First Edition For Equationhad Stopped My Progress In Tensor Notation For Introduction To Geometry Wyzant Resources Introduction To Geometry Geometry Is A Subject In Mathematics That Focuses On The Study Of Shapes, Sizes, Relative Configurations, And Spatial Properties Derived From The Greek Word Meaning Earth Measurement, Geometry Is One Of The Oldest Sciences It Was First Formally Organized By The Greek Mathematician Euclid AroundBC When He Arrangedgeometric Propositions Intobooks, Introduction To Geometry Lessons Geometry Terms Introduction To Geometry Lesson Plans By Anna Warfield In The Early Grades, Students Start Recognizing, Naming, And Drawing Shapes As Students Becomeadvanced, Geometry Becomescomplicated Part Of This Includes Understanding The Properties And Characteristics Of Shapes And Their Relation To One Another The Following Activities Aim To Help Students Master These Concepts AndIntroduction To Algebraic Geometry Introduction To Algebraic Geometry Introduction To Algebraic Geometry Toggle Navigation Introduction To Algebraic Geometry Introduction To Algebraic Geometry News Archive Return Results OfPageofResults Per Page No News Introduction To Algebraic Geometry Basic Data Detailed Data Classes Consultations Schedule CodeECTSLecturers In Charge Prof Dr ScAnalytic Geometry Wikipedia Pierre De Fermat Also Pioneered The Development Of Analytic Geometry Although Not Published In His Lifetime, A Manuscript Form Of Ad Locos Planos Et Solidos Isagoge Introduction To Plane And Solid Loci Was Circulating In Paris In , Just Prior To The Publication Of Descartes Discourse For context, I'm pretty involved in math competitions and have a safe index for the USAJMO this year. So this is coming from a competition math perspective. If your question is "I'm a school teacher, should I be using this book in my Honors Geometry class?" then the answer is definitely yes. This book is probably much better than any alternative you're considering. But if your question is "I want to personally get good at geometry for math competitions," that's when I can't exactly recommend this book.

I didn't rate this book poorly because it's a bad book, by any means. But this is probably one of the most overrated math textbooks out there. It's not bad, it's in fact far above average and I would definitely prefer this over any school textbook. It has competition problems too, which aligns with my own philosophy of "you can only remember hard stuff by doing hard problems." It's also a decent place to pick up the basics, but the book's structure doesn't lend itself to it. In fact, to use this book optimally, you probably have to actively go against the design of this book.

The pacing of the book is very slow and it's very hard to slog through. Unless you're a complete beginner to competition geometry, you're probably better off just picking stuff up from doing problems. That's not to say you can't pick up problems from doing them in the bookthe book has a quite decent selection of them. But actually reading the text should be treated as a last resort. (This is what my opinion is in general, but in this case I feel it much more strongly.)

This might be due to personal preference, but the structuring of the book is terrible. Things that do not deserve to be chapters are artificially inflated in length, and chapter labeling tries to be clever at the expense of clarity. Specific complaint: "Special Parts of Triangles" (otherwise known as "Triangle Centers" or "Cevians," both of those would've been fine). And the book takes up far too much time and space with stuff that really needs to be stated succinctly: "A perpendicular bisector of a segment is the locus of points equidistant from its endpoints," and "An angle bisector of two lines is the locus of points equidistant from those two lines." The proofs are also oneliners"Notice triangle X is congruent to triangle Y." And this kind of stuff needs to be made succinct to stand out. The use of oneway proofs instead of just a biconditional argument that encompasses the whole thing is also terribly inefficient and teaches bad habits. (There are some USAMO/IMO problems where proving one direction and proving the other are actually two separate nontrivial tasks, but this is rare and being able to biconditionally prove something with one sweeping argument is still good.) And worst of all, there's no way to tell what the most important facts are: The four triangle centers and the four cevians. (Perpendicular bisector isn't a cevian, but my point stands.) In a good manuscript I should be able to, without effort, tell what the triangle centers are, and the gist of their existence/property proofs. For this one it's very hard to tell.

The book also treats people like idiots, maybe because it's just "geometry standard" (even though nobody actually good at math cares what the "standard" is). The book insists on saying things like "SAS congruence" or "HL congruence" or whatever. Stuff that can be and should be oneliners aren't. What this book doesn't seem to understand is this: You don't need to spell out all of the trivial details. Just leave enough for the reader to be able to (somewhat) quickly pick it up on their own. Wellknown theorems are presented as "problems," so the fact that they're well known and the fact that they aren't novel/interesting, just necessary to build upon, is not communicated at all to the reader.

Even though I harp on this book, I realize that the reason it's so praised is in part because it deserves to be. It's also very hard to write a good introduction to geometrymy attempts have also ended up being much more suited to people who already have some experience (though I do try to make my manuscript beginner friendly)! So I think the world is made a much better place with this book rather than without, because this book fills a void that really needs to be filled. But it's not the holy grail and it's not the only way to get good at Geometry.

What do I recommend instead? I recommend doing lots of hard 2D geometry problems. You'll notice a patternat least in the AMC/AIME, it's not proving some triangle is similar to some other triangle or some angle is congruent to some other angle. In fact that part is usually trivial. The hard part is actually noticing what you need to prove, and convincing yourself that it's true instead of convincing yourself of some other stupid things. Consider PUMAC 2016/G7it's a very hard problem (which is why it's the secondtolast problem, after all), but not because we use some very obscure theorem that you have to read 100 textbooks to memorize. It's because the similar triangle (sorry, spoilers!) is very well hidden. What's even more amazing is that problems like these are oneliners. The gist of the solution to really, really hard geometry problems can just be summarized in 4,5 or 6 lines, which is really impressive considering how long harder Algebra/Geometry/Combinatorics problems are.

You might also hear people say that geometry is the most theoryheavy subject. This is true, in the context of the IMO. (There's also lots of theory in computational geometry, but AoPS Geometry doesn't even get a pass herethe stuff it presents is artificially inflated to look like more than it is, and the real meat doesn't even get included in there despite how easily and naturally it could be. Take Radical Axes for exampleat least tell everyone that the common chord of two circles bisects their common external tangent!)

In summary: This book is a good starting point for beginners, but it should not be treated as the holy grail and you should try to get away with using it as little as possible. This is the best high school geometry curriculum I've ever come across, and one of the only ones designed specifically for gifted math students. Topics are introduced using a discovery approacha problem is posed for the student to attempt on his or her own. Next, a solution is provided for clarity. In the process, theorems are discovered, which are then immediately used in solving the next problem(s), and so on. This is exactly the reverse approach that most geometry textbooks take (introducing theorems first, and only then showing why they are true)which really takes most of the fun and creativity of geometry out of the learning process. The discovery approach wouldn't work unless it were masterfully crafted, and indeed, the sequence of problems is no less than brilliant. Use this with your brightest math students and watch their faces light up! Geometry is often taught in a "memorize the theorems" approach and leaves it up to the students to attempt to solve problems (usually on the easier spectrum), absolutely not the case here. As expected from AoPS, the students are expected to attempt to discover the theorems and problem solving processes themselves using carefullycrafted problems which guide the students into doing so. This leads a much more deep understanding of geometric properties and theorems than what would come out of the average geometry curriculum. Simply putthe most amazing book on geometry I've ever come across.

P.S. AoPS discourages those stupid "twocolumn proofs" which is an absolute win.