Summarize · Induction · Proof without words · Coordinates · Complex numbers

Author: Ding Shisun
Publisher:
Publish Date: 1995-05-01
Features: This book is the fourth volume in Peking University's "Little Series of Mathematics—The Flowers of Wisdom." It contains selected, intriguing mathematical problems designed to spark interest in mathematics among high school and university students and provide engaging mental training. What constitutes "good mathematics" and what is "bad or not-so-good mathematics" is eloquently discussed by the renowned mathematician Chen Shengshen (see the book's content). The book features five short essays as examples of "good mathematics": "Gems of Wordless Proofs," "Mathematical Induction," "Recursive Sequences," "Coordinate Methods," and "Algebraic Equations of Any Degree." In contrast, it uses "Napoleon, Escher, and Plane Tiling Problems" as an example of "bad mathematics," aiming to provide useful materials for middle school mathematics teaching and extracurricular activities while minimizing detours in cultivating students' fundamental mathematical thinking skills. The article "A Note on the Principle of Mathematical Induction" highlights a widespread error in middle school mathematics both domestically and internationally: the Principle of Mathematical Induction is equivalent to the Least Natural Number Principle. To meet the needs of students participating in mathematical competitions, the book includes problems and solutions from the 33rd and 34th International Mathematical Olympiads. This book can serve as supplementary reading for high school students, middle school mathematics teachers, and lower-division university students, as well as for those interested in teaching. It also offers valuable guidance for students aspiring to participate in mathematical competitions.