Features

• Clear and concise explanations
• Difficult concepts are explained in simple terms
• Illustrated with graphs and diagrams

Table of Contents

Geometry Background

• Euclidean Geometry
• Euclidean Space
• Line
• Line Segment
• Incidence of planes and lines
  • Incidence Structure
• Euclidean Distance
  • One-dimensional distance
  • Two-dimensional distance
  • Three-dimensional distance
• Postulate
• The Plane Areas of Mathematics
• Translation
• Translational Symmetry
• Similarity

Triangles

• Triangle
  • Types of triangles
  • Points, lines and circles associated with a triangle
  • Computing the area of a triangle
  • Using vectors
  • Using trigonometry
  • Using coordinates
  • Using Heron's formula
  • Ceva's Theorem
  • Heron's Formula
• Equilateral Triangle
• Right Angle
• Pythagorean Theorem
• Pythagorean Triple
• Heronian Triangle
• Triangle Inequality
• Pedoe's Inequality
• Similar triangles

Parallel Lines

• Congruence
• Parallel Postulate

Polygons

• Convex polygon
• Internal Angle
• Diagonal
• Perimeter
• Quadrilateral
  • Isosceles Trapezoid
  • Parallelogram
  • Kite
  • Rhombus, Rhomboid
  • Rectangle
  • Square
  • Cyclic Quadrilateral, Brahmagupta's formula
  • Tangential Quadrilateral
• Star Polygon

Circles

• Analytic results
• Properties
• Calculating the parameters
• Area of a Disk
• Circular Sector
• Circular Segment
• Circumference
• Nine-point Circle

Transformational Geometry

• Scaling
• Rotation,
  • Euler's Formula,
  • Rotation Matrix,
  • Quaternions and Spatial Rotation
• Reflection
  • Coordinate Rotations and Reflections
• Linear Map

Solid Geometry

• Dihedral angle and Solid angle
• The Cube
  • Cuboid
  • Hypercube Graph
  • Parallelepiped
• Prisms
• The Tetrahedron and Pyramid
• Octahedron, Dodecahedron, Icosahedron
• Cones and Cylinders
• The Sphere and Spheroid,
• Quadrics:
  • Ellipsoid
  • Paraboloid
  • Hyperboloid