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Download e-book for kindle: 1089 and All That: A Journey Into Mathematics by David Acheson

By David Acheson

ISBN-10: 0199590028

ISBN-13: 9780199590025

David Acheson's impressive little ebook makes arithmetic available to all people. From extremely simple beginnings he is taking us on an exhilarating trip to a few deep mathematical rules. at the approach, through Kepler and Newton, he explains what calculus quite potential, supplies a short historical past of pi, or even takes us to chaos conception and imaginary numbers. each brief bankruptcy is thoroughly crafted to make sure that not anyone gets misplaced at the trip. full of puzzles and illustrated through international recognized cartoonists, this can be probably the most readable and resourceful books on arithmetic ever written.

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Extra info for 1089 and All That: A Journey Into Mathematics

Example text

Leonhard Euler (1707–1783) Take a sheet of paper ruled with straight lines a distance d apart, and drop on to it a straight pin, also of length d. Then the probability that the pin will lie across one of the lines is 2/π. No pins to hand? Then you could try tossing a coin a few times. ) If you toss a coin 2n times, where n is very large, then the probability of getting exactly n heads and exactly n tails is approximately . No coins either? Then you could just ask two friends to choose a lot of whole numbers; the probability that any two positive integers, chosen at random, have no common factor (other than 1) is 6/π2.

We then generate still more of these fractions by dividing each unit into three equal parts … and so on. And we might well imagine that by dividing up each unit into a larger and larger number of smaller and smaller equal parts we can reach eventually all the numbers on the line in this way. But we can’t. e. numbers which can be written as a ratio of two integers. It turns out that there are other numbers – called irrational numbers – that cannot be written in this way. And is one of them. makes things whiter!

In particular, if we have a circle of radius r, then circumference = 2πr, and area = πr2. The first of these formulae is more or less what we mean by the number π. For if we regard it as ‘obvious’ that the circumference of a circle is proportional to its diameter, then the ratio will be a single number, the same for all circles. And that number is denoted by the symbol π. e. 2r, the formula circumference = 2πr then follows immediately. But the second formula, area = πr2, is quite a different matter.

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1089 and All That: A Journey Into Mathematics by David Acheson


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