The Book of NumbersSpringer Science & Business Media, 16 mar 1998 - 310 páginas In THE BOOK OF NUMBERS, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. THE BOOK OF NUMBERS features Conway and Guy's favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. "Our aim," the authors write, "is to bring to the inquisitive reader. . .an explanation of the many ways the word 'number' is used." They explore patterns that emerge in arithmetic, algebra, and geometry, describe these pattern' relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematician/writers could do. |
Índice
The Romance of Numbers | 1 |
Figures from Figures Doing Arithmetic and Algebra by Geometry | 27 |
What Comes Next? | 63 |
Famous Families of Numbers | 91 |
The Primacy of Primes | 127 |
Further Fruitfulness of Fractions | 151 |
Geometric Problems and Algebraic Numbers | 179 |
Imagining Imaginary Numbers | 209 |
Some Transcendental Numbers | 235 |
Infinite and Infinitesimal Numbers | 263 |
Index | 299 |
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algebraic numbers Amer angle answer approximations arithmetic Babylonian base bers binary binomial Cantor cards Catalan numbers Chapter circle complex numbers computed congruent count cubes cycle length decimal denominator diagonal digits divide Eisenstein integers equal equation Euler exactly example fact factor Farey series Faulhaber's formula Fibonacci numbers Ford circles formula fractions frieze patterns Gauss Gaussian Gaussian integer Gaussian primes geometrical gives Greek Hackenbush hex numbers hexagon instance irrational numbers logarithms long primes Martin Gardner Math mathematician mathematics Mersenne Mersenne primes modulo multiples names notation numbers Figure odd numbers ordinal numbers Pascal's triangle pentatope petals positive powers prime numbers Pythagorean quadratic quaternions rational numbers real numbers residue classes roots sequence shows shuffle square numbers square pyramid stella octangula Størmer surreal numbers t₁ tetrahedral number theorem there's transcendental triangular numbers whole number word zero