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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 m...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester, England :
Horwood Pub.,
2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
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| 001 | SCIDIR_ocn869282262 | ||
| 003 | OCoLC | ||
| 005 | 20231120111515.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 140128s2001 enka o 000 0 eng d | ||
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| 019 | |a 871225141 | ||
| 020 | |a 9780857099686 |q (electronic bk.) | ||
| 020 | |a 085709968X |q (electronic bk.) | ||
| 020 | |z 1898563691 | ||
| 020 | |z 9781898563693 | ||
| 035 | |a (OCoLC)869282262 |z (OCoLC)871225141 | ||
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| 100 | 1 | |a Barry, Patrick D. | |
| 245 | 1 | 0 | |a Geometry with trigonometry / |c by Patrick D. Barry. |
| 264 | 1 | |a Chichester, England : |b Horwood Pub., |c 2001. | |
| 300 | |a 1 online resource (xv, 235 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 applicationDescribes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architectureProvides many geometric diagrams for a clear understanding of the text and includes problem exercises for each chapter. | ||
| 505 | 0 | |a Front Cover; About the author; Dedication; Geometry with Trigonometry; Copyright Page; Table of Contents; Preface; Glossary; Chapter 1. Preliminaries; 1.1 HISTORICAL NOTE; 1.2 NOTE ON DEDUCTIVE REASONING; 1.3 EUCLID'S The Elements; 1.4 OUR APPROACH; 1.5 REVISION OF GEOMETRICAL CONCEPTS; 1.6 PRE-REQUISITES; Chapter2. Basic shapes of geometry; 2.1 LINES, SEGMENTS AND HALF-LINES; 2.2 OPEN AND CLOSED HALF-PLANES; 2.3 ANGLE-SUPPORTS, INTERIOR AND EXTERIOR REGIONS, ANGLES; 2.4 TRIANGLES AND CONVEX QUADRILATERALS; Chapter3. Distance; degree-measure of an angle; 3.1 DISTANCE; 3.2 MID-POINTS. | |
| 505 | 8 | |a 3.3 A RATIO RESULT3.4 THE CROSS-BAR THEOREM; 3.5 DEGREE-MEASURE OF ANGLES; 3.6 MID-LINE OF AN ANGLE-SUPPORT; 3.7 DEGREE-MEASURE OF REFLEX ANGLES; Chapter4. Congruence of triangles; parallel lines; 4.1 PRINCIPLES OF CONGRUENCE; 4.2 ALTERNATE ANGLES, PARALLEL LINES; 4.3 PROPERTIES OF TRIANGLES AND HALF-PLANES; Chapter5. The parallel axiom; Euclidean geometry; 5.1 THE PARALLEL AXIOM; 5.2 PARALLELOGRAMS; 5.3 RATIO RESULTS FOR TRIANGLES; 5.4 PYTHAGORAS' THEOREM, c. 550B.C.; 5.5 MID-LINES AND TRIANGLES; 5.6 AREA OF TRIANGLES, CONVEX QUADRILATERALS etc.; Chapter6. Cartesian coordinates. | |
| 505 | 8 | |a Applications6.1 FRAME OF REFERENCE, CARTESIAN COORDINATES; 6.2 ALGEBRAIC NOTE ON LINEAR EQUATIONS; 6.3 CARTESIAN EQUATION OF A LINE; 6.4 PARAMETRIC EQUATIONS OF A LINE; 6.5 PERPENDICULARITY AND PARALLELISM OF LINES; 6.6 ORTHOGONAL PROJECTION; 6.7 COORDINATE TREATMENT OF HARMONIC RANGES; Chapter7. Circles; their basic properties; 7.1 INTERSECTION OF A LINE AND A CIRCLE; 7.2 PROPERTIES OF CIRCLES; 7.3 FORMULA FOR MID-LINE OF AN ANGLE-SUPPORT; 7.4 POLAR PROPERTIES OF A CIRCLE; 7.5 ANGLES STANDING ON ARCS OF CIRCLES; 7.6 SENSED DISTANCES; Chapter8. Translations; axial symmetries; isometries. | |
| 505 | 8 | |a 8.1 TRANSLATIONS AND AXIAL SYMMETRIES8.2 ISOMETRIES; 8.3 TRANSLATION OF FRAME OF REFERENCE; Chapter9. Trigonometry; cosine and sine; addition formulae; 9.1 INDICATOR OF AN ANGLE; 9.2 COSINE AND SINE OF AN ANGLE; 9.3 ANGLES IN STANDARD POSITION; 9.4 HALF-ANGLES; 9.5 THE COSINE AND SINE RULES; 9.6 COSINE AND SINE OF ANGLES EQUAL IN MAGNITUDE; Chapter10. Complex coordinates; rotations, duo-angles; 10.1 COMPLEX COORDINATES; 10.2 COMPLEX-VALUED DISTANCE; 10.3 ROTATIONS AND AXIAL SYMMETRIES; 10.4 SENSED ANGLES; 10.5 SENSED-AREA; 10.6 ISOMETRIES AS COMPOSITIONS. | |
| 505 | 8 | |a 10.7 ORIENTATION OF A TRIPLE OF NON-COLLINEAR POINTS10.8 SENSED ANGLES OF TRIANGLES, THE SINE RULE; 10.9 SOME RESULTS ON CIRCLES; 10.10 ANGLES BETWEEN LINES; 10.11 A CASE OF PASCAL'S THEOREM, 1640; Chapter11. Vector and complex-number methods; 11.1 EQUIPOLLENCE; 11.2 SUM OF COUPLES, MULTIPLICATION OF A COUPLE BY A SCALAR; 11.3 SCALAR OR DOT PRODUCTS; 11.4 COMPONENTS OF A VECTOR; 11.5 VECTOR METHODS IN GEOMETRY; 11.6 MOBILE COORDINATES; 11.7 SOME WELL-KNOWN THEOREMS; 11.8 ISOGONAL CONJUGATES; Chapter12. Trigonometric functions in calculus; 12.1 REPEATED BISECTION OF AN ANGLE. | |
| 650 | 0 | |a Geometry. | |
| 650 | 0 | |a Trigonometry. | |
| 650 | 6 | |a G�eom�etrie. |0 (CaQQLa)201-0007174 | |
| 650 | 6 | |a Trigonom�etrie. |0 (CaQQLa)201-0007939 | |
| 650 | 7 | |a geometry. |2 aat |0 (CStmoGRI)aat300054529 | |
| 650 | 7 | |a trigonometry. |2 aat |0 (CStmoGRI)aat300054531 | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Geometry |2 fast |0 (OCoLC)fst00940864 | |
| 650 | 7 | |a Trigonometry |2 fast |0 (OCoLC)fst01156713 | |
| 776 | 0 | 8 | |i Print version: |a Barry, Patrick D. |t Geometry with trigonometry |z 1898563691 |w (OCoLC)48998003 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9781898563693 |z Texto completo |