Table of Contents

1. The Natural Numbers.
The Basics. The Fundamental Theorem of Arithmetic. Searching for Primes. Number Fascinations.

2. The Integers.
Diophantine Equations. Congruence Arithmetic. Pell and Pythagoras. Factoring Large Numbers.

3. The Rational Numbers.
Rational Numbers as Decimals. Decimals as Rational Numbers. Continued Fractions. Solving Equations on the Rational Plane

4. The Real Numbers.
Algebraic Representations. Geometric Representations. Analytic Representations. Searching for Transcendental Numbers.

5. Mathematical Projects.
Rings of Factors. Sums of Consecutive Numbers. Measuring Abundance. Inside the Fibonacci Numbers. Pictures at an Iteration. Eenie Meenie Miney Mo. Factoring with the Pollard …r Method. Charting the Integral Universe. Triangles on the Integral Lattice. The Gaussian Integers. Writing Fractions the Egyptian Way. Building Polygons with Dots. The Decimal Universe of Fractions, I. The Decimal Universe of Fractions, II. The Making of a Star. Making Your Own Real Numbers. Building 1 the Egyptian Way. Continued Fraction Expansions of x1/2 N. A Special Kind of Triangle. Polygon Numbers. Continued Fraction Expansions.