Geometry with Trigonometry

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 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

Content: Dedication , Page i ABOUT DR. PADDY BARRY , Page ii Front Matter , Page iii Copyright , Page iv Preface , Pages v-vi GLOSSARY , Pages xiv-xv 1 - Preliminaries , Pages 1-19 2 - Basic shapes of geometry , Pages 20-33 3 - Distance; degree-measure of an angle , Pages 34-46 4 - Congruence of triangles; parallel lines , Pages 47-56 5 - The parallel axiom; Euclidean geometry , Pages 57-73 6 - Cartesian coordinates; applications , Pages 74-93 7 - Circles; their basic properties , Pages 94-109 8 - Translations; axial symmetries; isometries , Pages 110-116 9 - Trigonometry; sine and cosine; addition formulae , Pages 117-132 10 - Complex coordinates; sensed angles; rotations; applications to circles; angles between lines , Pages 133-170 11 - Position vectors; vector and complex-number methods in geometry , Pages 171-215 12 - Trigonometric functions in calculus; mensuration of discs and circles , Pages 216-226 Appendix A - List of Axioms , Pages 227-228 References , Page 229 Index , Pages 230-235 Addresses a neglected mathematical area of which geometry and trigonometry form an important core component, as they underpin analysis in its manifold aspects and applications in classical applied mathematics and sundry types of science and engineering.