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Table of contents

Why does this one have more than two hundred-or is it four thousand?

Numerical Analyst Nick Trefethen on the pleasures and significance of his subject

The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples.

David Foster Wallace. Zero: The Biography of a Dangerous Idea. Charles Seife. Popular math at its most entertaining and enlightening. The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics.

The Art of the Infinite: The Pleasures of Mathematics - Ellen Kaplan - Google книги

Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.

In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics.

Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang.

Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.

Out of the Labyrinth: Setting Mathematics Free. Robert Kaplan. For any reader who has felt the excitement of mathematical discovery-or tried to convey it to someone else-this volume will be a delightful and valued companion.

Paul J. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. David Foster Wallace. Zero: The Biography of a Dangerous Idea.

Bibliographic Information

Charles Seife. Popular math at its most entertaining and enlightening. The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics.

For zero, infinity's twin, is not like other numbers.


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It is both nothing and everything. In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics.

The Art of the Infinite: The Pleasures of Mathematics

Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang.

Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything. Out of the Labyrinth: Setting Mathematics Free. Robert Kaplan. For any reader who has felt the excitement of mathematical discovery-or tried to convey it to someone else-this volume will be a delightful and valued companion. Paul J. Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma.

The Art of the Infinite: The Pleasures of Mathematics

In An Imaginary Tale, Paul Nahin tells the year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. The Pleasures of Counting is a book about people working with mathematics and challenges they have faced. The book has pages with a total of 19 chapters and 3 appendices. It contains a lot of material and is split into five parts: The uses of abstraction, Meditations on measurement, The pleasures of computation, Enigma variations, and The pleasures of thought.

It addresses history, short biographies, mathematical theories, physics, biology, to name some.

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Topics touched upon are: Finding the source of a cholera outbreak, effects of medicine, submarines and convoys during World War I, production of ammunition, using radar, hitting moving aircrafts, attacking submarines from aircrafts during WWII, the early days of operational research, body mass and metabolic rate in animals, dimensional analysis in physics, properties of light, boat anchor design, Einstein's theory of relativity, weather prediction, turbulence, analysing the causes of war, measuring the length of coast lines, blood flow in vessels, pencil-and-paper vs.

Every subject treated in the book is in some way related to mathematics. Most of the mathematics, however, are simple equations and back-of-the-envelope considerations. But many mathematical disciplines are touched upon, some of them being: Gathering and interpreting data, first and second order linear differential equation, trigonometry, curve-fitting using polynomials, Taylor expansions, numerical integration, the differentiability of functions, probability theory, fractals, number representations, Euclid's algorithm, Fibonacci numbers, maximum flow in networks, sorting and finding the largest number, roots and inequalities for second-degree polynomials, Stirling's estimate of n!

Think carefully about the arguments against convoy given above. Which seem to you valid, which invalid and which partially valid? Give your reasons. Are there any other arguments for or against which ought to have been considered?