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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 |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester, England :
Horwood Pub.,
2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.