This book addresses a neglected mathematical area where basic geometry underpins undergraduate and graduate courses. Its interdisciplinary portfolio of applications includes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architecture. Professor Barry, from his long experience of teaching and research, here delivers a modern and coherent exposition of this subject area for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of application. Euclidean geometry is neglected in university courses or scattered over a number of them. This text emphasises a systematic and complete build-up of material, moving from pure geometrical reasoning aided by algebra to a blend of analytic geometry and vector methods with trigonometry, always with a view to efficiency. The text starts with a selection of material from the essentials of Euclidean geometry at A level, and ends with an introduction to trigonometric functions in calculus.
Very many geometric diagrams are provided for a clear understanding of the text, with abundant Problem Exercises for each chapter. Students, researchers and industrial practitioners would benefit from this sustained mathematisation of shapes and magnitude from the real world of science which can raise and help their mathematical awareness and ability.
- Provides a modern and coherent exposition of geometry with trigonometry for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of application- Describes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architecture- Provides many geometric diagrams for a clear understanding of the text and includes problem exercises for each chapter
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Preliminaries; Basic shapes of geometry; Distance; Degree-measure of angles; Congruence of triangles; Parallel lines; The parallel axiom; Euclidean geometry; Cartesian co-ordinates; Applications; Circles and their basic properties; Translations; Axial symmetries; Isometries; Trigonometry; Sine and cosine; Sensed angles; Rotations; Vector and complex number methods; Trigonometric functions in calculus; List of axioms; References and index.
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