Old and New Unsolved Problems in Plane Geometry and Number Theory

Old and New Unsolved Problems in Plane Geometry and Number Theory presents a collection of mathematical problems that remain unresolved despite centuries of effort by mathematicians. The book covers problems from two major branches of mathematics - plane geometry and number theory - with a focus on questions that can be stated in simple terms but have proven difficult to solve. The text provides historical context and background for each problem, tracing attempts at solutions through different eras and mathematical approaches. Each chapter includes discussions of related solved problems, partial results, and connections between different mathematical concepts. The problems range from ancient geometric puzzles to modern questions in number theory that emerged from computer-based research. The book includes detailed explanations of mathematical concepts and techniques, along with illustrations and diagrams to aid understanding. This work highlights the persistence of mathematical mystery and demonstrates how seemingly straightforward questions can lead to deep insights about the nature of mathematics. The selected problems reveal the continuous evolution of mathematical thought and the ongoing dialogue between classical and contemporary approaches.

Readers describe this as a specialized reference book that collects challenging math problems, with many requiring advanced knowledge of geometry and number theory. Readers liked: - Clear explanations of each problem's history - Mix of ancient and modern unsolved problems - Rigorous mathematical presentation - Extensive references and bibliography Common criticisms: - Graduate-level math background needed for most problems - Some solutions/discussions are too brief - Price point is high for length Ratings: Goodreads: 4.0/5 (5 ratings) Amazon: No reviews available MathOverflow users reference it positively in discussions of open problems From a MathOverflow review: "The problems are well-chosen and span different difficulty levels. However, many require significant mathematical maturity beyond undergraduate studies." A Goodreads reviewer notes: "Not for casual reading - this is a serious mathematical text that demands focus and prerequisite knowledge."

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🔷 The book explores 24 major unsolved problems, some dating back to ancient Greece, and others that were still unsolved when the book was published in 1991 (though a few have since been solved). 🔷 Stan Wagon is not just a mathematician - he's also known for building and riding a square-wheeled bicycle that can roll smoothly on a specially designed road made of catenary curves. 🔷 The book connects two seemingly different mathematical fields - plane geometry and number theory - showing how problems in one area often have surprising connections to the other. 🔷 One of the featured problems, the "moving sofa problem" (finding the largest sofa that can be moved around a corner), remains unsolved after more than 50 years and has applications in robotics and industrial design. 🔷 The author includes recreational mathematics problems alongside serious mathematical conjectures, making complex concepts accessible while maintaining academic rigor.