Mathematical Fallacies, Flaws, and Flimflam

Front Cover
MAA, Jun 15, 2000 - Mathematics - 167 pages
0 Reviews
Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Numbers
1
Whose real world?
2
United in purpose
3
A case of black and whitebut not so much black
4
Effects of changing temperature
5
Distributing addition over multiplication
6
An exponential mess
7
A divisibility property
8
Where the grass is greener
78
How to make a million
80
A problem of Lewis Carroll
81
Nontransitive dice
82
Three coins in the fountain
83
Getting black balls
84
The car and goats and other problems
86
Your lucky number is in Pi
90

Why Wiles proof of the Fermat Conjecture is false
9
A quick ? proof of irrationality
10
How the factorial works
11
Algebra and Trignometry
15
A superficial volume problem
16
How to solve a quadratic equation
17
An old method for solving a cubic
18
An exponential equation
19
The multiplication rules for logarithms
20
An application of the CauchySchwarz Inequality
21
Factoring homogeneous polynomials
22
The zero polynomial
23
An inductive fallacy
24
On not identifying equations and identities
25
A surd equation
27
The disappearing solution
28
Solving an inequality
31
An appearance of finite geometric sequences
32
Floored by an Olympiad problem
33
A New Identity for the Ceiling Function
34
Geometry
37
A luney way to square a circle
39
The SteinerLehmus Theorem
41
A geometry problem
42
A case of irregularity
43
A counterexample to Morleys Theorem
45
Going for the stars
46
The speeders delight
48
A solution to problem 480
50
Tangency by double roots
51
A puzzling graph
52
The wilting lines
54
The height of a trapezoid
55
Forces with a given resultant
56
A linear pythagorean theorem
57
The surface area of a sphere
59
Volume of a tin can
60
The Puptent Problem
61
The spirit is willing but the ham is rotten
62
Finite Mathematics
63
All positive integers are equal
64
Four weighings suffice
65
There is a unique positive integer
66
Doggedly bisexual
67
Equal unions
68
Surjective functions
69
Spoiled for choice
70
A full house
71
Which balls are actually there?
72
Red and blue hats
73
An invalid argument
74
A logical paradox
75
Probability
77
Limits and Derivatives
91
The shortest distance from a point to a parabola
92
A foot by any other name
93
A degree of differentiation
94
The derivative of the sum is the sum of the derivatives
95
Double exponential
96
Calculation of a limit
98
Which is the correct asymptote?
99
Every derivative is continuous
101
Telescoping series
102
Integration and Differential Equations
103
The integral of log sin x
104
Evaluation of a sum
105
Integrals of products
106
LHopitals Rule under the integral sign
107
Why integrate?
108
The disappearing factor
109
A positive vanishing integral
110
Average chord length
111
Area of an ellipse
112
An Euler equation
113
Solving a secondorder differential equation
114
Power series thinning
115
Multivariate and Applications
117
Polar paradox?
118
Evaluating double integrals
119
The converse to Eulers theorem on homogeneous functions
120
The wrong logarithm
121
The conservation of energy according to Escher
122
Calculating the average speed
123
Hanging oneself with a minimum of rope
124
Generalizing an approach to the radius of curvature
126
Linear and Modern Algebra
129
The SchwarzCauchy Inequality
130
An entrance examination question
131
An inversion conundrum
132
The CayleyHamilton Theorem
133
All groups are simple
134
Groups with separate identities
135
The number of conjugates of a group element
136
Even and odd permutations
137
How large is the set of degenerate real symmetric matrices?
139
Advanced Undergraduate Mathematics
141
The countability of the reals
142
A consequence of the nearness of rationals to reals
143
A universal property of real subsets
144
A topological spoof
145
Is there a nonmeasurable set?
146
The continuum hypothesis
147
A heavyduty proof that 10
148
Parting Shots
151
References
161
Copyright

Other editions - View all

Common terms and phrases

References to this book

Bibliographic information