How Euler Did Even More

253 Pages·2014·3.701 MB·English

by  C. Edward Sandifer

How Euler Did Even More
(cid:2)C 2015by
TheMathematicalAssociationofAmerica,Inc.
LibraryofCongressCatalogCardNumber2014953563
PrinteditionISBN:978-0-88385-584-3
ElectroniceditionISBN:978-1-61444-519-7
How Euler Did Even More
C. Edward Sandifer
Western Connecticut State University
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Contents
Preface....................................................................... xi
Part 1: Geometry.................................................. 1
1 TheEulerLine(January2009).............................................. 3
2 AForgottenFermatProblem(December2008)............................... 10
3 AProductofSecants(May2008)........................................... 18
4 CurvesandParadox(October2008)......................................... 26
5 DidEulerProveCramer’sRule?(November2009—AGuestColumnby
RobBradley).............................................................. 32
Part II: Number Theory.......................................... 39
6 Factoring F (March2007)................................................. 41
5
7 RationalTrigonometry(March2008)........................................ 45
8 Sums(andDifferences)thatareSquares(March2009)........................ 52
Part III: Combinatorics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
9 St.PetersburgParadox(July2007).......................................... 61
10 LifeandDeath–Part1(July2008).......................................... 67
11 LifeandDeath–Part2(August2008)....................................... 74
Part IV: Analysis ............................................... 81
12 e,π andi:Whyis“Euler”intheEulerIdentity(August2007)................. 83
13 Multi-zetaFunctions(January2008)......................................... 88
14 SumsofPowers(June2009)................................................ 95
15 ATheoremofNewton(April2008).........................................101
ix