Introducing Infinity
A Graphic Guide
Published on 1. December 2014
176 pages
978-1-84831-883-0 (ISBN)
Description
Infinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers - and provoked and shocked others.
The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers.
Brian Clegg and Oliver Pugh's brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.
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09/2012
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Persons
Brian Clegg is a popular science writer whose Dice World and A Brief History of Infinity were both longlisted for the Royal Society Prize for Science Books. He has written for publications including Nature, The Times and BBC Focus.
Content
- Intro
- Cover
- Title Page
- Copyright
- Contents
- Big numbers
- Googoled
- Symbols from India
- The Book of Calculation
- 0, a powerful tool
- Archimedes: The Sand Reckoner
- The poetry of infinity
- Number sequences
- Strange sequences
- The infinity machine
- Zeno's paradoxes
- Achilles and the tortoise
- Apeiron
- Aristotle
- Potential infinity
- Left brain/right brain
- The power of algebra
- Visual thinking
- Pythagorean perfection
- Diagonals of a square
- Drowning by numbers
- Squaring the circle
- Transcendental pi
- Infinity of pi
- Omega
- Not really numbers at all?
- God and the infinite
- The human perspective
- "Only a manner of speaking"
- Galileo
- Infinity on wheels
- Back to geometry
- The normal rules don't apply
- The infinity of 1?
- A common error
- The indivisibles
- Newton and potential infinity
- Fluxions
- From o to 0
- Leibniz's calculus
- Newton vs. Leibniz
- Notation
- Differential and integral calculus
- Battling Bishop Berkeley
- The infidel mathematician
- Dividing zero by zero
- Flow and change
- Tending towards zero
- Finding a symbol
- The Möbius strip and Klein bottle
- Bolzano and real infinity
- Cantor: mind-bending infinity
- The joy of sets
- Venn diagrams
- Boolean algebra
- Making sets of the world
- Peano and the cardinals
- Russell's paradox
- Cantor and subsets
- Imaginary numbers
- Aleph null
- Cardinals and ordinals
- Ordinal infinity
- Countably infinite
- Cantor's elegant proof
- Covering the number line
- Another Cantor proof
- Points in space
- The shock of the infinite
- Power sets
- Cantor under attack
- Cantor succumbs
- Gödel's shocking proof
- Back to the continuum hypothesis
- Does infinity exist?
- Fractal infinity
- Recursion
- Fractals in nature
- Measuring the coastline
- The Cantor set
- An infinite universe?
- Edge of the universe?
- Quantum infinity
- The slit experiment
- Spin
- The infinitesimal
- Non-standard analysis
- Infinitesimals and Brownian motion
- Hilbert's Hotel
- Gabriel's Horn
- The jungle of infinity
- Glossary
- Further Reading
- Author's acknowledgements
- Artist's acknowledgements
- About the Authors
- Index
