Author(s): V. Gusev, V. Litvinenko, A. Mordkovich
Publisher: Mir Publishers
Year: 1988
Language: English
Pages: 238
City: Moscow
Front Cover
Title Page
PREFACE
CONTENTS
Chapter 1 PLANE GEOMETRY
SEC. 1. METHODS OF SOLVING GEOMETRICAL PROBLEMS
I. Triangles and Quadrilaterals
II. Circles
III. Areas of Plane Figures
SEC. 2. TRIANGLES AND QUADRILATERALS
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
I. Right Triangles
II. Isosceles Triangles
III. Arbitrary Triangles
IV, Parallelograms
V. Trapezoids
VI. Miscellaneous Problems
SEC. 3. CIRCLES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
I. Circles
II. Inscribed and Circumscribed Triangles
III. A Circle and a Triangle Arranged Arbitrarily
IV. A Circle and a Quadrilateral
V. Miscellaneous Problems
SEC. 4. AREAS OF PLANE FIGURES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
I. Area of Triangles
II. Area of Quadrilaterals
III. Area of Polygons
IV. Area of Combined Figures
V. Miscellaneous Problems
SEC. 5. GEOMETRICAL TRANSFORMATIONS
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
I. Symmetry with Respect to a Point
II. Symmetry About a Straight Line
III. Rotation
IV. Translation
V. Homothetlc Transformation
SEC. 6. VECTORS
I. Affine Problems
II. Metric Problems
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
I. Addition and Subtraction of Vectors.Multiplication of a Vector by a Number
II. Scalar Product of Vectors
III. Miscellaneous Problems
SEC. 7. GREATEST AND LEAST VALUES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
Chapter 2 SOLID GEOMETRY
SEC. 8. CONSTRUCTING THE REPRESENTATION OF A GIVEN FIGURE
SEC. 9. GEOMETRICAL CONSTRUCTIONS IN SPACE
I. Simplest Constructions in Space
II. Loci of Points
III. Applications of Certain Loci of Points and Straight Lines
IV. Constructions on Representations
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
I. Simplest Constructions in Space
II. Loci of Points
III. Applications of Certain Loci of Points and Lines
IV. Constructions on Representations
(1) Constructing Plane Figures in Space
(2) Section of a Polyhedron by a Plane Parallel to Two Straight Lines
(3) Cons tructing a Perpendicular to a Straight Line and a Perpendicular to a Plane
(4) Section of a Polyhedron by a Plane PassingThrough a Given Point Perpendicular to a Given Line
(5) Constructing a Locus of Points Equidistant from Given Points
SEC. 10. SKEW LINES. ANGLE BETWEEN A STRAIGHT LINE AND A PLANE
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
SEC. 11. DIHEDRAL AND POLYHEDRAL ANGLES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
SEC. 12. SECTIONS OF POLYHEDRONS
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
SEC. 13. SURFACES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
SEC. 14. VOLUMES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
SEC. 15. COMBINATIONS OF POLYHEDRONS AND CIRCULAR SOLIDS
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
SEC. 16. GREATEST AND LEAST VALUES
PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE!
ANSWERS AND HINTS
Chapter 1
Chapter 2
Back Cover
