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Ideal for users who may have little previous experience with abstraction and proof, this book provides a rigorous and unified--yet straightforward and accessible --exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme--the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes--with a leisurely development that allows ample time for mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular. Focus on one main topic--The axiomatic development of the absolute plane--which is pursued through a classification into Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the "gap" plane. Gradually presents axioms for absolute plane geometry.
"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.
This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.
Dive into the world of shapes, lines, and angles with "Plane Geometry" by G. A. Wentworth, a comprehensive guide that unlocks the mysteries of geometric principles and their practical applications. Embark on a journey of discovery as you explore the fundamental concepts of plane geometry, from the properties of triangles and quadrilaterals to the intricacies of circles and polygons. Through clear explanations and illustrative diagrams, Wentworth demystifies complex geometric principles, making them accessible to readers of all levels. Themes of symmetry, proportion, and spatial reasoning are woven throughout this engaging text, offering readers valuable insights into the underlying structure of the world around them. Whether you're studying for an exam or simply eager to expand your mathematical horizons, "Plane Geometry" provides the tools you need to succeed. Delve into the fascinating world of geometric proofs and theorems, where logic and reasoning reign supreme. With Wentworth as your guide, you'll learn how to construct convincing arguments and solve challenging problems with confidence and precision. With its practical approach and real-world examples, "Plane Geometry" goes beyond the classroom, offering readers valuable insights into the practical applications of geometric principles in fields such as architecture, engineering, and computer graphics. Whether you're designing a building or plotting a course for a spacecraft, the principles of plane geometry are essential tools for success. Since its publication, "Plane Geometry" has been hailed as a classic text on the subject, earning praise for its clarity, depth, and relevance. Its ability to demystify complex concepts while inspiring readers to explore the beauty of geometry makes it a must-have resource for students, educators, and anyone with a passion for mathematics. Whether you're a seasoned mathematician or a curious novice, "Plane Geometry" promises to expand your horizons and deepen your understanding of the world around you. So, pick up your copy today and embark on a journey of mathematical discovery with G. A. Wentworth as your guide. Don't miss your chance to master the principles of plane geometry and unlock a world of mathematical possibilities. Grab your copy of "Plane Geometry" today and take the first step towards mathematical mastery.
The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of 'play' in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.