To Infinity and Beyond: A Cultural History of the InfiniteSpringer Science & Business Media, 1 de dez. de 2013 - 284 páginas The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. . . - David Hilbert (1862-1943) Infinity is a fathomless gulf, There is a story attributed to David Hilbert, the preeminent mathe into which all things matician whose quotation appears above. A man walked into a vanish. hotel late one night and asked for a room. "Sorry, we don't have o Marcus Aurelius (121- 180), Roman Emperor any more vacancies," replied the owner, "but let's see, perhaps and philosopher I can find you a room after alL" Leaving his desk, the owner reluctantly awakened his guests and asked them to change their rooms: the occupant of room #1 would move to room #2, the occupant of room #2 would move to room #3, and so on until each occupant had moved one room over. To the utter astonish ment of our latecomer, room #1 suddenly became vacated, and he happily moved in and settled down for the night. But a numbing thought kept him from sleep: How could it be that by merely moving the occupants from one room to another, the first room had become vacated? (Remember, all of the rooms were occupied when he arrived. |
Conteúdo
2 | |
Zero One Infinity | 6 |
Towards Legitimation | 10 |
Numbers Large and Small | 14 |
Convergence and Limit | 17 |
The Prime Numbers | 21 |
The Fascination of Infinite Series | 26 |
The Geometric Series | 29 |
Some Functions and Their Graphs | 68 |
Some Geometric Paradoxes Involving Infinity | 83 |
Inversion in a Circle | 88 |
Geographic Maps and Infinity | 95 |
Tiling the Plane | 102 |
A New Look at Geometry | 108 |
Aesthetic Infinity | 135 |
The Magic World of Mirrors | 149 |
More about Infinite Series | 34 |
An Excursion into the Number Concept | 40 |
The Discovery of Irrational Numbers | 44 |
π and eThree Celebrated Irrationals | 50 |
Cantors New Look at the Infinite | 54 |
Beyond Infinity | 60 |
Geometric Infinity | 67 |
Maurits C EscherMaster of the Infinite | 164 |
The Modern Kabbalists | 179 |
The Horizons Are Receding | 199 |
The Expanding Universe | 212 |
Which Way from Here? | 227 |
257 | |
Outras edições - Ver todos
To Infinity and Beyond: A Cultural History of the Infinite - New Edition Eli Maor Visualização parcial - 2017 |
Termos e frases comuns
angle artist astronomer Axiom of Choice axioms Bruno calculus Cantor circle concept converge counting numbers curve decimal denumerable digit discovery distance earth entire equal equation Escher Heirs c/o Euclid's Euclidean Euclidean geometry example fact Figure finite formula fractions function galaxies Gauss geometric series Greek harmonic series Heirs c/o Cordon infinite number infinite sets infinite universe integers intersection inversion irrational numbers known limit logarithmic spiral M.C. Escher M.C. Escher Heirs mathematician mathematics mirrors Möbius strip motion natural numbers non-Euclidean geometry number line object original paradox parallel lines Parallel Postulate pattern physical plane point at infinity prime number projective geometry proof rational numbers real numbers reflection regarded regular polygons Reprinted segment sequence set theory sides smaller space sphere square stars straight line subset surface symbol symmetry groups telescope tessellation theorem tion triangle zero