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