Book Tutor — Zadania z olimpiad matematycznych z całego świata. Planimetria i stereometria (math olympiad problems, plane and solid geometry)

Book Tutor — Zadania z olimpiad matematycznych z całego świata. Planimetria i stereometria is a collection of competition-style geometry problems focused on plane geometry (planimetry) and solid geometry (stereometry). Published by Tutor, the book gathers tasks from international math olympiads and similar contests, intended to develop problem-solving skills, geometric reasoning, and proof techniques. The compilation is arranged to support independent study as well as guided preparation for mathematics competitions.

Advantages

The book provides a broad selection of carefully selected problems that illustrate core methods in planar and spatial geometry, including constructions, angle and length relations, and three-dimensional reasoning. Each task emphasizes logical argumentation and solution strategies commonly found in olympiad settings. The structured presentation supports progressive learning: problems range in difficulty and include opportunities to practice both routine and creative approaches to geometric proofs.

Suitable for

• Students preparing for math olympiads and mathematical competitions
• High-school and advanced middle-school learners studying geometry
• Teachers and coaches compiling problem sets for training sessions
• Self-learners seeking to improve geometric proof techniques and spatial visualization

Key specifications

• Subject focus: planar geometry (planimetry) and solid geometry (stereometry)
• Content type: collection of olympiad-style problems with illustrative solutions or solution sketches where provided
• Intended audience: students, teachers, coaches, and self-learners
• Language of problems: Polish (original title), with mathematical notation and diagrams typical for competition problems
• Use case: study, practice, contest preparation, classroom assignment

How to use

Approach the book by selecting problems matched to current skill level and gradually increasing difficulty. Read each problem carefully, attempt a personal solution before consulting provided answers or hints, and write full, justified proofs to build rigorous reasoning. Use diagrams to visualize planar and spatial configurations, and rework solved tasks using alternative methods to deepen understanding. Teachers can assign targeted problem sets for lessons or weekly training, while coaches can use the collection to design timed practice sessions.

Usage recommendations

For effective preparation, combine regular problem-solving sessions with review of fundamental theorems in Euclidean geometry, practice drawing precise figures, and discuss multiple solution approaches with peers or mentors. Maintain a solutions notebook to track methods, common techniques, and typical pitfalls when working on planimetry and stereometry tasks.