The Little Book of Mathematical Principles, Theories, & Things [1 ed.] 1504800532, 9781504800532, 9781607652229

Table of contents :
Writing Numbers
Fractions
Quadratic Equations
The Greatest Pyramid
π
The Pythagoreans
Pythagoras’s Theorem
Irrational Numbers
Perfect Numbers
Regular Polygons
Platonic Solids
The Golden Ratio
Trisecting the Angle
Doubling the Cube
Squaring the Circle
Zeno’s Paradoxes
Plato and Platonism
Conic Sections
Euclid’s Elements
The Fifth Postulate
Sum of the Angles in a Triangle
The Fundamental Theorem of Arithmetic
The Infinity of Prime Numbers
Measurement of a Sphere
Quadrature of the Parabola
The Sand Reckoner
Trigonometry
Negative Numbers
The Earth-Centered Universe
Zero
Kitab wa al jabr wa al muqabalah (The Book of Shifting and Balancing)
Cubic Equations – Geometric Solutions
Fibonacci Numbers
Perspective
Cubic Equations – Algebraic Solution
Quartic Equations
The Sun-Centered Universe
Mathematical Induction
Falling Bodies
The Sun-Centered Universe Again
Logarithms
Tessellations
Regular Solids Revisited
Calculating Machines
Analytic Geometry
A Formula for Prime Numbers
The Problem of the Points
Pascal’s Triangle
The Binomial Distribution
Pascal’s Wager
Differentiation
Integration
The Fundamental Theorem of Calculus
Three Laws of Motion
The Law of Gravity
The Precession of the Equinoxes
The Law of Large Numbers
The Normal Distribution
The Seven Bridges of Königsberg
Goldbach’s Conjecture
V + F = E + 2
The Gambler’s Fallacy
Complex Numbers
e
Regular Polygons Revisited
Arithmetic and Geometric Progressions
The Fundamental Theorem of Algebra
Fourier Series
The Difference and Analytic Engines
Quintic Equations
Non-Euclidean Geometry
Galois Theory
Constructible Lengths
Doubling the Cube and Trisecting the Angle Revisited
Quaternions
Transcendental Numbers
Kirkman’s Schoolgirl Problem
The Laws of Thought
Twisted Shapes
The Riemann Hypothesis
Maxwell’s Equations
The Countability of Fractions
The Uncountability of the Reals
Squaring the Circle Revisited
The Correlation Coefficient
The Continuum Hypothesis
Space-Filling Curves
Wallpaper Patterns
‘Doughnuts and Coffee Cups’
What the Tortoise Said to Achilles
The Prime Number Theorem
Hilbert’s Problems
Quantum Mechanics
The Central Limit Theorem
Russell’s Paradox
Mathematics as Part of Logic
The Snowflake Curve
Axiom of Choice
The Jordan Curve Theorem
Special Relativity
Intuitionism
Zermelo–Fraenkel Set Theory
The Hairy-Ball Theorem
General Relativity
The Hilbert Program
Gödel’s Theorem
The Travelling Salesman
Turing Machines
Binary Numbers
The Ham Sandwich Theorem
The Enigma Machine
Colossus
Game Theory
ENIAC
The Prisoner’s Dilemma
Electronic Calculators
Polya’s Principles
Erdös Number
Chaos Theory
The Secretary Problem
Catastrophe Theory
Life
Matiyasevich’s Theorem
P = NP?
Public Key Codes
Fractals
The Four-Color Theorem
The Logistic Model
Stacking Oranges
Fermat’s Last Theorem
The Seven Millennium Prize Problems
Appendix
Glossary
Acknowledgements
Index