- #1
- 22,183
- 3,325
- Author: Serge Lang and Gene Murrow
- Title: Geometry
- Amazon Link: https://www.amazon.com/dp/1441930841/?tag=pfamazon01-20
- Prerequisities: High-school algebra
- Level: High school
Table of Contents:
Code:
[LIST]
[*] Introduction
[*] Distance and Angles
[LIST]
[*] Lines
[*] Distance
[*] Angles
[*] Proofs
[*] Right Angles and Perpendicularity
[*] The Angles of a Triangle
[*] An Application: Angles of Reflection
[/LIST]
[*] Coordinates
[LIST]
[*] Coordinate Systems
[*] Distance Between Points on a Line
[*] Equation of a Line
[/LIST]
[*] Area and the Pythagoras Theorem
[LIST]
[*] The Area of a Triangle
[*] The Pythagoras Theorem
[/LIST]
[*] The Distance Formula
[LIST]
[*] Distance Between Arbitrary Points
[*] Higher Dimensional Space
[*] Equation of a Circle
[/LIST]
[*] Some Applications of Right Triangles
[LIST]
[*] Perpendicular Bisector
[*] Isosceles and Equilateral Triangles
[*] Theorems About Circles
[/LIST]
[*] Polygons
[LIST]
[*] Basic Ideas
[*] Convexity and Angles
[*] Regular Polygons
[/LIST]
[*] Congruent Triangles
[LIST]
[*] Euclid's Tests for Congruence
[*] Some Applications of Congruent Triangles
[*] Special Triangles
[/LIST]
[*] Dilations and Similarities
[LIST]
[*] Definition
[*] Change of Area Under Dilation
[*] Change of Length Under Dilation
[*] The Circumference of a Circle
[*] Similar Triangles
[/LIST]
[*] Volumes
[LIST]
[*] Boxes and Cylinders
[*] Change of Volume Under Dilations
[*] Cones and Pyramids
[*] The Volume of the Ball
[*] The Area of the Sphere
[/LIST]
[*] Vectors and Dot Product
[LIST]
[*] Vector Addition
[*] The Scalar Product
[*] Perpendicularity
[*] Projections
[*] Ordinary Equation for a Line
[*] The 3- Dimensional Case
[*] Equation for a Plane in 3-Space
[/LIST]
[*] Transformations
[LIST]
[*] Introduction
[*] Symmetry and Reflections
[*] Terminology
[*] Reflection Through a Line
[*] Reflection Through a Point
[*] Rotations
[*] Translations
[*] Translations and Coordinates
[/LIST]
[*] Isometries
[LIST]
[*] Definitions and Basic Properties
[*] Relations with Coordinates
[*] Composition of Isometries
[*] Definition of Congruence
[*] Proofs of Euclid's Tests for Congruent Triangles
[*] Isometries as Compositions of Reflections
[/LIST]
[*] Index
[/LIST]
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