Book:Ian Stewart/Incredible Numbers

Contents

 * Preface


 * Numbers


 * Small Numbers
 * $1 \quad$ The Indivisible Unit
 * $2 \quad$ Odd and Even
 * $3 \quad$ Cubic Equation
 * $4 \quad$ Square
 * $5 \quad$ Pythagorean Hypotenuse
 * $6 \quad$ Kissing Number
 * $7 \quad$ Fourth Prime
 * $8 \quad$ Fibonacci Cube
 * $9 \quad$ Magic Square
 * $10 \quad$ Decimal System


 * Zero and Negative Numbers
 * $0 \quad$ Is Nothing a Number?
 * $-1 \quad$ Less Than Nothing


 * Complex Numbers
 * $i \quad$ Imaginary Number


 * Rational Numbers
 * $\frac 1 2 \quad$ Dividing the Indivisible
 * $\frac {22} 7 \quad$ Approximation to $\pi$
 * $\frac {466} {885} \quad$ Tower of Hanoi


 * Irrational Numbers
 * $\sqrt 2 \sim 1.414213 \quad$ First Known Irrational
 * $\pi \sim 3.141592 \quad$ Circle Measurement
 * $\phi \sim 1.618034 \quad$ Golden Number
 * $e \sim 2.718281 \quad$ Natural Logarithms
 * $\frac {\log 2} {\log 3} \sim 1.584962 \quad$ Fractals
 * $\frac \pi {\sqrt{18} } \quad$ Sphere Packing
 * $\sqrt [12] 2 \sim 1.059463 \quad$ Musical Scale
 * $\zeta \left({3}\right) \sim 1.202056 \quad$ Apéry's Constant
 * $\gamma \sim 0.577215 \quad$ Euler's Constant


 * Special Small Numbers
 * $11 \quad$ String Theory
 * $12 \quad$ Pentominoes
 * $17 \quad$ Polygons and Patterns
 * $23 \quad$ Birthday Paradox
 * $26 \quad$ Secret Codes
 * $56 \quad$ Sausage Conjecture
 * $168 \quad$ Finite Geometry


 * Special Big Numbers
 * $26! = 403,291,461,126,605,635,584,000,000 \quad$ Factorials
 * $43,252,003,274,489,856,000 \quad$ Rubik Cube
 * $6,670,903,752,021,072,936,960 \quad$ Sudoku
 * $2^{57,885,161} - 1$ (total of $17,425,170$ digits) $\quad$ Largest Known Prime


 * Infinite Numbers
 * $\aleph_0 \quad$ Smallest Infinity
 * $c \quad$ Cardinality of Continuum


 * Life, the Universe, and ...
 * $42 \quad$ Not Boring at All


 * Further Reading
 * Figure Acknowledgements