The book A Course in Old and New Geometry II: Basic Euclidean Geometry provides a detailed exploration of Euclidean geometry and it focuses on circles and their properties, with a particular emphasis on Thales' Theorem and its applications. The book effectively integrates historical perspectives, providing readers with a sense of the evolution of geometric thought. This context enriches the learning experience and emphasizes the relevance of Euclidean geometry.
It begins with a clear statement of Thales' Theorem: "The angle in a semicircle is a right angle." This is followed by a precise mathematical formulation and a historical overview of Thales of Miletus, including anecdotes about his life and contributions to geometry. The historical context enriches the mathematical discussion, providing insight into the origins of logical proof and the significance of Thales' work in the development of mathematics.
It explores extensions and generalizations of Thales' Theorem, such as the relationship between the position of a triangle's vertex relative to a circle and the type of angle formed (acute, obtuse, or right). The "Strong Thales' Theorem" and its corollaries are introduced, providing a more comprehensive framework for understanding the theorem's implications.
The language is precise and formal, appropriate for a mathematical text. Mathematical notation and terminology are used consistently and correctly. Definitions and theorems are clearly stated, and proofs are logically structured. Including diagrams is highly beneficial, but their descriptions could be more detailed to ensure a full interpretation of them without ambiguity.
Overall, A Course in Old and New Geometry II: Basic Euclidean Geometry provides a thorough and engaging exploration of Euclidean geometry, with a focus on Thales' Theorem and its applications. It is well-suited for readers with a foundational understanding of geometry and an interest in the historical and theoretical aspects of the subject.
very informative book