Archimedes' Revenge: The Joys and Perils of Mathematics - download pdf or read online

By Paul Hoffman

ISBN-10: 0449217507

ISBN-13: 9780449217504

An creation to the delights and demanding situations of recent arithmetic.

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Extra info for Archimedes' Revenge: The Joys and Perils of Mathematics

Sample text

Imagine the sequence of consecutive numbers n! + 2, n! + 3, n! + 4, and so on all the way to n! + n. Now, the first term in the sequence, n! + 2, is evenly divisible by 2; the second term, n! + 3, is evenly divisible by 3; the third term, n! + 4, is evenly divisible by 4; and so on. There are n - I numbers in this sequence, and none is a prime number. By choosing n to be as large as you want, you can have a prime-free sequence of consecutive whole numbers as long as you want. Prime-rich sequences, however, are also abundant.

110 IS 10 40 907 1 1: 114 n 107U r R Ia. ll tlIHO N. 4,41 717 n? nn 1 nu 7 l~l ? 11e 114, 110? 1011 lI 4,8 I-n 111 414BY,7 skIon"l 14111a Rn R*n 0 Rn 9117S 17 a E8 1 04? 1 4 7Dnn Rn 04,1 Dn* 14 171121 14 lIe 117, jw Ia. 0111 inn inn 151? Ia. ll1919 1 2111l| t tD u3? :7 a nI jl i 91112 pn 11 14inn ? IUi D 894 m 1114, 4,89 l 1 I ni1 ? 1114 111 211 2 a~ I"llS 1173n41 1217 4, 101 0117illtm il n141 1106 917 SI Rn S ln 1in is, wni a. tnt me iMl"1 Wl1 Iiiiiii*1' nn 14 41n Ra Ian n 919 1111, R IlMi t a?

Yellow cows = ('/6 + 1/7) white herd. " Stripped to its mathematical essentials, the problem so far is to solve seven equations that involve eight unknowns (four groups of bulls specified by color and four groups of cows of corresponding color). It turns out that these equations are not hard to solve. Indeed, they admit infinitely many solutions, the smallest involving a total herd of 50,389,082 cattle, a number that could comfortably graze on Sicily's 6,358,400 acres. Archimedes, however, did not stop there.

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Archimedes' Revenge: The Joys and Perils of Mathematics by Paul Hoffman


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