Famous problems of elementary geometry

Author: Shen Yibing
Publisher:
Publish Date: 2005-07-01
Features: This book is a lecture manuscript by the renowned mathematician F. Klein delivered in G?ttingen, Germany, in 1894. It primarily discusses the three famous classical geometric problems—squaring the cube, trisecting an angle, and squaring the circle. At the time, the author explained the topic in a clear and accessible manner, eliciting excellent responses from the audience. Later, it was edited and published with the help of German mathematicians, and it was translated into English in 1930,. Although the content of this book dates back over 100 years, the methods explained by the master are still considered elegant and concise today, offering valuable reference for modern mathematics. The three classical geometric problems remain a subject of blind research in China, which is why the new high school teaching standards have incorporated related content. This book holds significant reading value for university students, secondary school teachers, and even middle school students, as well as serving as a reference for faculty and scientists in higher education institutions. The book includes five chapters: algebraic equations solvable by square roots, the Delian problem and trisecting an angle, dividing the circle, the geometric construction of a regular 17-sided polygon, and Cantor's proof of the existence of transcendental numbers.