Problem-Solving and Selected Topics in Euclidean Geometry - Olympiad

In this review of Problem-Solving and Selected Topics in Euclidean Geometry the bottom line is clear: this book is for serious students and coaches preparing for mathematical olympiads who want a focused collection of methods and problems. The authors present a disciplined, method-driven approach that highlights key ideas before full solutions, so readers can learn not only solutions but the thought process behind them. This review finds the book most valuable as a study companion for advanced high school students, contest trainers, and anyone seeking deeper problem-solving tools in Euclidean geometry.

Key Features

• Theorem collection: A curated set of theorems particularly useful for solving olympiad-style problems, allowing readers to reference relevant results quickly.
• Method emphasis: Detailed discussion of analysis, synthesis, construction and proof helps readers understand multiple avenues to approach a single problem.
• Key ideas before solutions: Each problem is prefaced by a guiding idea so learners can attempt a solution independently using the intended insight.
• Selected olympiad problems: Problems that appeared in olympiads and shortlists are discussed, giving context and real contest-level practice.
• Contributions from experts: Additional problems proposed by leading mathematicians broaden the scope beyond contest archives.

Who It's For

This book is aimed at advanced high school students preparing for national or international mathematical olympiads, coaches who need a compact source of techniques and worked examples, and undergraduates who want to deepen their problem-solving toolbox in Euclidean geometry. The structure suits readers who can commit to careful study and practice rather than casual browsing.

Those seeking a beginner introduction to geometry, a classroom textbook with exercises for every section, or a broad survey of modern geometry topics should look elsewhere; this volume emphasizes olympiad methods and selected problems rather than comprehensive pedagogical coverage.

Pros & Cons

Pros

• Concentrated presentation of useful theorems makes it a practical reference for contest problem solving.
• The emphasis on multiple methods trains flexible thinking across analysis and synthesis techniques.
• Key ideas before full solutions encourage active problem solving rather than passive reading.

Cons

• Not designed as an elementary textbook, so readers without prior geometry background may find it challenging.
• The focus on olympiad-style problems limits its usefulness as a general course companion for all students.

Specifications

Title	Problem-Solving and Selected Topics in Euclidean Geometry
Authors	Sotirios E. Louridas, Michael Th. Rassias
Subject	Euclidean geometry and olympiad problem solving
Content focus	Theorems, methods, selected olympiad problems and proposed problems
Approach	Key idea presentation followed by full solutions
Intended audience	Advanced students, coaches, contest trainers

Our Verdict

This book is a high-value, focused resource for anyone seriously preparing for geometry contests or seeking to deepen problem-solving skills; its method-first layout and curated problems make it an effective study companion, though it is best suited to readers with an existing geometry foundation.

Frequently Asked Questions

Does this book include full solutions?
Yes, each problem is presented with a key idea first and then a complete solution, so readers can attempt the problem before reading the full proof.

Is this suitable for beginners?
Not ideal for beginners; it assumes prior knowledge of basic Euclidean geometry and is targeted at advanced students and contest preparation.

Are the problems from real olympiads?
Selected problems include those given in mathematical olympiads and shortlists, plus additional problems proposed by experts.