Problems in Geometry – A. Kutepov, A. Rubanov

Stanje proizvoda: papirnati ovitak lošije, ostalo lijepo očuvano.

The book contains a collection of 1351 problems (with answers) in plane and solid geometry for technical schools and colleges. The problems are of varied content, involving calculations, proof, construction of diagrams, and determination of the spatial location of geometrical points. It gives sufficient problems to meet the needs of students for practical work in geometry, and the requirements of the teacher for varied material for tests, etc.

CHAPTER I. REVIEW PROBLEMS

1. The Ratio and Proportionality of Line Segments,
Similarity of Triangles 7
2. Metric Relationships in a Right-Angled Triangle 10
3. Regular Polygons, the Length of the Circumference
and the Arc 15
4. Areas of Plane Figures 17

CHAPTER II. SOLVING TRIANGLES

5. Solving Right-Angled Triangles 22
6. Solving Oblique Triangles 29
Law of Cosines 29
Law of Sines 31
Areas of Triangles, Parallelograms and
Quadrilaterals 32
Basic Cases of Solving Oblique Triangles 34
Particular Cases of Solving Oblique Triangles 34
Heron’s Formula 35
Radii r and R of Inscribed and Circumscribed Circles and the Area S of a Triangle 36
Miscellaneous Problems 37

CHAPTER III. STRAIGHT LINES AND PLANES IN SPACE

7. Basic Concepts and Axioms. Two Straight Lines in Space 43
8. Straight Lines Perpendicular and Inclined to a Plane 46
9. Angles Formed by a Straight Line and a Plane 52
10. Parallelism of a Straight Line and a Plane 55
11. Parallel Planes 59
12. Dihedral Angles. Perpendicular Planes 63
13. Areas of Projections of Plane Figures 67
14 Polyhedral Angles 69

CHAPTER IV. POLYHEDRONS AND ROUND SOLIDS

15. Prisms and Parallelepipeds 71
16. The Pyramid 77
17. The Truncated Pyramid 81
18. Regular Polyhedrons 84
19. The Right Circular Cylinder 86
20. The Right Circular Cone 89
21. The Truncated Cone 93