Professional mathematicians, of course, regard this " trick" as mathematically . David Acheson's latest book " and All That" (Oxford University Press ) is an original attempt at Download PDF version | Printer friendly version. Jan 1, January and all that - a journey into mathematics. For David Acheson, the "elements of mystery and surprise run through a great. and All That: A Journey into Mathematics and millions of other books are available for Amazon Kindle. This item and All That: A Journey into Mathematics by David Acheson Paperback $ Start reading and All That: A Journey into Mathematics on your Kindle in under.
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Here are some of his most popular titles: The Colossal Book of Mathematics Gardner has collected articles from his year old archive of Scientific American articles. The result is this amazing compendium. Classic Brainteasers A collection of favourite puzzles and games.
Entertaining Mathematical Puzzles Some excellent games and riddles to lose yourself in. Dover Mathematics Books This publisher has an excellent reputation for their wide range of mathematics books. Here are just a few of their most popular titles: Great Problems of Elementary Mathematics By Heinrich D-Orrie A puzzle book that has lost none of its ingenuity in its translation from French to English. A Concise History of Mathematics By Dirk Jan Struik An interesting and accessible guide to some of the greatest mathematicians and the remarkable findings they have made.
Rouse Ball Last re-printed in , this is an authoritative account of the history of mathematics.
Eves An interesting, accessible and thorough account. Games, Gods and Gambling A study into the history of statistics. Zero By Charles Seife An account of one of the simplest, yet most complicated of ideas in mathematics — the number zero.
For nearly two hundred years no one could find anything wrong with this proposition. Nobody could actually prove it, either, but it had been around for a very long time, and it had been proposed, after all, by a very respected authority And then, in , L. Lander and T.
Attempting to generalise in mathematics on the basis of one or two special cases is always a risky business, of course, and one of the most telling examples I know involves an apparently innocent little problem in geometry. Take a circle, mark n points on the circumference, and join each point to all the others by straight lines.
This divides the circle into a number of different regions, and the question is: how many? It is assumed that no more than two lines intersect at any point inside the circle.
Now, for the first few values of n, namely 2, 3, 4 and 5, the number of regions follows a very simple pattern: 2, 4, 8 and But it isn't. It's 31! And the general formula for the number of regions isn't the simple one we had in mind at all.
Surprising connections In higher mathematics, some of the deepest surprises come about from unexpected connections between apparently quite different parts of the subject. When we first meet the number , for instance, it is all about circles. In particular, if we take any circle, then is the ratio of circumference to diameter. Imagine the surprise, then, in the mid17th century, when Leibniz discovered the following extraordinary connection between and the odd numbers: While it is possible to prove this result, beyond all doubt, using the methods of calculus, I have yet to meet anyone who can explain this connection between circles and the odd numbers in truly simple terms.
Surprising connections and all that Sometimes, however, the surprising connection lies not within mathematics itself, but between mathematics and real world. The ellipse, for instance, is a curve that was well known to Greek mathematicians, and it can be constructed by pulling a loop of string round two fixed points. These points, H and I, are called focal points.
At first sight, perhaps, this is "just" geometry. Yet, some 1, years after the ellipse's first appearance in this way, the German astronomer Kepler discovered that the planets move around the Sun in elliptical orbits, and as if that were not coincidence enough the Sun is always at one of the focal points! In , Robert Orenstein implemented Vesterman's encoding for online play at www.
For many years, that page was apologizing for having "temporarily" shut down its terse interactive features, since Mathematical Intelligencer 24 1 Winter Here's one way to present the effect: If we use a regular deck of cards, we either remove the face cards or attribute to them the same value 1 as aces.
All told, only a few cards are thus singled out as special. The majority are not You may play this version online with a computer which honestly shuffles the deck.
Allow yourself to be baffled a few times before reading on Well, the explanation is simply statistical. You are instructed to pick any word in the first red section of the text. Then, skip as many words as there are letters in your chosen word.
For example, if you picked the fourth word "Course" you have to skip 6 words "of human Events, it becomes necessary" to end up on the word "for" Iterate the same process, by skipping as many words as there are letters in the successive words you land on.
What's the first word you encounter in the last green section? The sequence would continue with the words: descent, that, causes.
The "magic" is based on the Kruskal principle discussed above The words that do work have been underlined for you.