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eMath 3: Geometry

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Overview: This book gives an overview of the basic concepts of plane geometry, and describes the theory of triangles, general polygons, and circles. It continues with an overview of solid geometry, with applications to cylinders, cones and spheres.

Table of contents:

1 Preface
2 Basic Concepts of Plane Geometry
2.1 Points and Lines
2.2 Angles
3 Triangles
3.1 Definition of a Triangle
3.2 Various Triangles
3.3 The Pythagorean Theorem
3.4 Special Points of a Triangle
3.5 The Trigonometry of a Right Triangle
3.6 The Laws of Sines and Cosines
4 Polygons
4.1 Definition of a Polygon
4.2 Similarity and Scale
4.3 Parallelograms and Special Cases
4.4 Regular Polygons
5 Circles
5.1 Properties of Circles and Pi
5.2 The Tangent of a Circle
5.3 Inscribed Angles
6 Basic Concepts of Solid Geometry
6.1 Cuboid
6.2 Geometric Solids in Space
6.3 An Extension of Plane Geometry to Solid Geometry
7 Cylinders
7.1 Prisms
7.2 Circular Cylinders
7.3 The Volume of Similar Solids
8 Cones
8.1 Pyramids
8.2 Cones
8.3 Frusta
9 Spheres
9.1 Basic Concepts of Spheres
9.2 Parts of a Sphere