Overview of "Trigonometry: A Very Short Introduction" by Glen Van Brummelen

Key Themes:

1. Connection to Science: The book explores how trigonometry has become an indispensable tool in predicting cyclic patterns such as animal populations and ocean tides, highlighting its significance in modern science.
2. Historical Journey: It delves into the historical development of trigonometry, tracing its journey through major cultures such as medieval India and the Islamic World, and its interactions with disciplines like geography and religious practice.
3. Mathematical Developments: The book discusses trigonometry's role in the most startling mathematical developments of the modern world, including its interactions with the concept of infinity and the birth of complex numbers.
4. Non-Euclidean Geometries: It explores how trigonometry allows us to explore non-Euclidean geometries, opening up possibilities for the shape of space itself, and how spherical geometry takes us back to ancient Greek astronomers and European navigators.

Plot Summary: The book provides a concise and accessible introduction to trigonometry, covering its historical evolution, its applications in science, and its contributions to modern mathematical discoveries. It explains how trigonometry has been used across various cultures and how it has influenced the development of mathematics and science. The narrative is structured to make complex mathematical concepts highly readable and engaging.

Critical Reception:

• Positive Reception: The book has received positive reviews for its ability to connect trigonometry to broader scientific and cultural contexts. Reviewers have praised Van Brummelen's clear and engaging writing style, making the subject accessible to readers with varying levels of mathematical background.
• Historical Depth: The book's historical sections have been particularly well-received for their comprehensive and detailed coverage of the subject's evolution across different cultures and time periods.

Conclusion

"Trigonometry: A Very Short Introduction" by Glen Van Brummelen offers a unique blend of historical context, mathematical insight, and scientific application, making it an excellent resource for those interested in understanding the significance and scope of trigonometry. The book's concise and engaging style makes it suitable for both beginners and those looking to deepen their knowledge of the subject.