Number, Shape And Symmetry

The Triangle Game
Practice Problem Solutions and Hints
Exercises
The Beginnings Of Number Theory
Setting the Table: Numbers, Sets, and Functions
Rules of Arithmetic
A New System
One's Digit Arithmetic
Practice Problem Solutions and Hints
Exercises
Axioms In Number Theory
Consequences of the Rules of Arithmetic
Inequalities and Order
Practice Problem Solutions and Hints
Exercises
Divisibility And Primes
Divisibility
Greatest Common Divisor
Primes
Practice Problem Solutions and Hints
Exercises
The Division And Euclidean Algorithms
The Division Algorithm
The Euclidean Algorithm and GCDs
The Fundamental Theorem of Arithmetic
Practice Problem Solutions and Hints
Exercises
Variations On A Theme
Applications of Divisibility
More Algorithms
Practice Problem Solutions and Hints
Exercises
Congruences And Groups
Congruences
Groups and Other Structures
Practice Problem Solutions and Hints
Exercises
Applications Of Congruences
Divisibility Tests
Days of the Week
Check Digits
Practice Problem Solutions and Hints
Exercises
Rational Numbers And Real Numbers
Fractions to Decimals
Infinity
Rational Numbers
Irrational Numbers
How Many Real Numbers? Practice Problem Solutions and Hints
Exercises
Introduction To Geometry
Practice Problem Solutions and Hints
Exercises
Polygons And Their Construction
Polygons and Their Angles
Constructions
Practice Problem Solutions and Hints
Exercises
Symmetry Groups
Symmetric Motions of the Triangle
Symmetric Motions of the Square
Symmetries of Regular n-gons
Practice Problem Solutions and Hints
Exercises
Permutations
Symmetric Motions as Permutations
Counting Permutations and Symmetric Groups
Even More Economy of Notation
Practice Problem Solutions and Hints
Exercises
Polyhedra
Regular Polyhedra
Euler's Formula
Symmetries of Regular Polyhedra
Reflections and Rotations
Variations on a Theme: Other Polyhedra
Practice Problem Solutions and Hints
Exercises
Tessellations
Tessellating with a Single Shape
Tessellations with Multiple Shapes
Variations on a Theme: Polyominoes
Frieze Patterns
Infinite Patterns in Two and Three Dimensions
Practice Problem Solutions and Hints
Exercises
Connections
Fibonacci Numbers and the Golden Mean
Constructible Numbers and Polygons
Practice Problem Solutions and Hints
Exercises
Appendix: Euclidean Geometry Review
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