Geometry and Its Applications

Geometry and Its Applications is a textbook that combines traditional geometry with a contemporary approach, focusing on real-world applications. It introduces axiomatic, Euclidean, and non-Euclidean geometry and integrates applications and examples throughout. The Third Edition offers updates, expanded coverage of historical notes, and nearly 300 applications from various fields, making it suitable for engineering and science majors, as well as future mathematics teachers.

Format: Hardback
Length: 473 pages
Publication date: 20 June 2022
Publisher: Taylor & Francis Ltd

This groundbreaking textbook seamlessly blends traditional geometry with a contemporary approach, firmly rooted in real-world applications. It skillfully balances a deductive approach with discovery learning, introducing axiomatic, Euclidean, and non-Euclidean geometries, while seamlessly integrating transformational geometry. Throughout, the text seamlessly incorporates applications and examples, enhancing its accessibility and relevance. The Third Edition boasts numerous updates, including expanded historical notes, a comprehensive treatment of axiomatic geometry, a vast array of nearly 300 applications spanning diverse fields, and a strong emphasis on computer science-related applications, captivating the interest of students. Additionally, a multitude of new exercises keep the presentation fresh and engaging.

Geometric concepts have long been fundamental to understanding the world around us. From the ancient Greeks to modern mathematicians, the study of shapes, angles, and dimensions has played a crucial role in advancing scientific knowledge and engineering. In this textbook, we will explore the rich history and applications of geometry, from its theoretical foundations to its practical implementations.

Chapter 1: Introduction to Geometry
In this chapter, we will begin by discussing the historical origins of geometry and its development over time. We will examine the contributions of ancient Greek mathematicians such as Euclid and Pythagoras, who laid the foundation for modern geometry. We will also explore the different branches of geometry, including Euclidean geometry, non-Euclidean geometry, and transformational geometry.

Chapter 2: Euclidean Geometry
In this chapter, we will delve into the principles of Euclidean geometry, which is based on a set of axioms and postulates. We will discuss the properties of lines, angles, planes, and solids, and how they are used to construct geometric figures and shapes. We will also explore the concepts of congruence, similarity, and symmetry, which are fundamental to Euclidean geometry.

Chapter 3: Non-Euclidean Geometry
In this chapter, we will explore the principles of non-Euclidean geometry, which deviates from the Euclidean axioms and postulates. We will examine the properties of curved surfaces, such as circles, ellipses, and hyperbolic planes, and how they are used to construct geometric figures and shapes. We will also explore the concept of parallelism, which is not a fundamental concept in Euclidean geometry.

Chapter 4: Transformational Geometry
In this chapter, we will explore the principles of transformational geometry, which is a branch of geometry that focuses on the transformation of geometric figures. We will discuss the properties of rigid transformations, such as translations, rotations, and reflections, and how they are used to construct geometric figures and shapes. We will also explore the concept of homography, which is a transformation that preserves the length of lines.

Chapter 5: Applications of Geometry
In this chapter, we will explore the diverse applications of geometry in various fields, including engineering, physics, and computer science. We will examine how geometric concepts are used to design and analyze structures, such as buildings, bridges, and airplanes. We will also explore how geometric concepts are used to solve mathematical problems, such as optimization and differential equations.

Chapter 6: Conclusion
In this chapter, we will summarize the key concepts and principles of geometry that we have covered in the previous chapters. We will discuss the importance of geometry in understanding the world around us and its potential for future advancements. We will also provide a list of resources for further study and exploration of geometry.

In conclusion, this textbook provides a comprehensive and engaging introduction to the world of geometry. It blends traditional geometry with a contemporary approach, firmly rooted in real-world applications. By exploring the principles of Euclidean, non-Euclidean, and transformational geometry, students will gain a deep understanding of the fundamental concepts of geometry and its practical applications. Whether you are a student of mathematics, engineering, or any other field, this textbook is an invaluable resource for furthering your knowledge and understanding of geometry.

Weight: 942g
Dimension: 226 x 276 x 33 (mm)
ISBN-13: 9780367187989
Edition number: 3 ed