Professor Stewart’s Hoard of Mathematical Treasures

Ian Stewart

Publisher:

Basic Books

Publication Date:

2010

Number of Pages:

352

Format:

Paperback

Price:

16.95

ISBN:

9780465017751

Category:

General

MAA Review
Table of Contents

[Reviewed by

Allen Stenger

, on

02/27/2010

]

The introduction accurately describes this book as a “mathematical miscellany,” with an emphasis on “miscellaneous.” It is aimed primarily at general readers, but also has things that will interest mathematicians. It is a continuation of Stewart’s previous miscellany, Professor Stewart’s Cabinet of Mathematical Curiosities.

The content is primarily brain-teasers with some mathematical angle (full solutions are included), but also has a lot of fun math facts and curiosities, along with some (possibly apocryphal) stories about mathematicians, some jokes, a little bit of physics (angular momentum is a recurring theme), and some real mathematics. This is not a book for scholars: there are no references and no index, and no attempt to trace the history of the items. There are a number of references to online sites (especially Wikipedia) for further reading.

i believe none of the items here is original, although some of the treatments may be. Most items will be familiar to mathematicians, especially those who pay any attention to recreational math. Some items that I thought were especially interesting: a good explanation (with photos) of how cats always land on their feet; the three-jugs problem (interesting because it gives a systematic solution using trilinear coordinates); and a good explanation of the scientific basis and mathematical modeling of global warming.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning.

Acknowledgements

Second Drawer Down

Calculator Curiosity 1
Year Turned Upside Down
Luckless Lovelorn Lilavati
Sixteen Matches
Swallowing Elephants
Magic Circle
Dodgem
Press-the-Digit-ation
Secrets of the Abacus
Redbeard’s Treasure
Hexaflexagons
Who Invented the Equals Sign?
Stars and Snips
By the Numbers of Babylon
Magic Hexagons
The Collatz-Syracuse-Ulam Problem
The Jeweller’s Dilemma
What Seamus Didn’t Know
Why Toast Always Falls Buttered-Side Down
The Buttered Cat Paradox
Lincoln’s Dog
Whodunni’s Dice
A Flexible Polyhedron
But What About Concertinas?
The Bellows Conjecture
Digital Cubes
Nothing Which Appeals Much to a Mathematician
What Is the Area of an Ostrich Egg?
Order into Chaos
Big Numbers
The Drowning Mathematician
Mathematical Pirates
The Hairy Ball Theorem
Cups and Downs
Secret Codes
When 2 + 2 = 0
Secret Codes That Can Be Made Public
Calendar Magic
Mathematical Cats
The Rule of Eleven
Digital Multiplication
Common Knowledge
Pickled Onion Puzzle
Guess the Card
And Now with a Complete Pack
Halloween = Christmas
Egyptian Fractions
The Greedy Algorithm
How to Move a Table
Rectangling the Square
Newton, by Byron
X Marks the Spot
Whatever’s the Antimatter?
How to See Inside Things
Mathematicians Musing About Mathematics
Wittgenstein’s Sheep
Leaning Tower of Pizza
PieThagoras’s World-Famous Mince πs
Diamond Frame
Poor Relations
Alexander’s Horned Sphere
The Sacred Principle of Mat
Perfectly Abundantly Amicably Deficient
Target Practice
Just a Phase I’m Going Through
Proof Techniques
Second Thoughts
How Dudeney Cooked Loyd
Cooking with Water
Celestial Resonance
Calculator Curiosity 2
Which is Bigger?
Sums That Go On For Ever
The Most Outrageous Proof
Colorado Smith and the Solar Temple
Why Can’t I Add Fractions Like I Multiply Them?
Farey, Farey, Quite Contrary
Pooling Resources
Welcome to the Rep-Tile House
Cooking on a Torus
The Catalan Conjecture
The Origin of the Square Root Symbol
Please Bear with Me
The Ham Sandwich Theorem
Cricket on Grumpius
The Man Who Loved Only Numbers
The Missing Piece
The Other Coconut
What Does Zeno?
Pieces of Five
Pi in the Sky
The Curious Incident of the Dog
Mathematics Made Difficult
A Weird Fact about Egyptian Fractions
A Four Colour Theorem
Serpent of Perpetual Darkness
What Are the Odds?
A Potted History of Mathematics
The Shortest Mathematical Joke Ever
Global Warming Swindle
Name the Cards
What Is Point Nine Recurring?
Ghost of a Departed Quantity
Nice Little Earner
A Puzzle for Leonardo
Congruent Numbers
Present-Minded Somewhere Else
It’s About Time
Do I Avoid Kangaroos?
The Klein Bottle
Accounting the Digits
Multiplying with Sticks
As Long as I Gaze on Laplacian Sunrise
Another Take on Mathematical Cats
Bordered Prime Magic Square
The Green-Tao Theorem
Peaucellier’s Linkage
A Better Approximation to π
Strictly for Calculus Buffs
The Statue of Pallas Athene
Calculator Curiosity 3
Completing the Square
The Look and Say Sequence
Non-Mathematicians Musing About Mathematics
Euler’s Conjecture
The Millionth Digit
Piratical Pathways
Trains that Pass in the Siding
Please Make Yourself Clear
Squares, Lists and Digital Sums
Hilbert’s Hit-List
Match Trick
Which Hospital Should Close?
How to Turn a Sphere Inside Out
A Piece of String Walked into a Bar…
Slicing the Cake
The Origin of the Symbol for Pi
Hall of Mirrors
Greek and Trojan Asteroids
Sliding Coins
Beat That!
Euclid’s Puzzle
The Infinite Monkey Theorem
Monkeys Against Evolution
Universal Letter of Reference
Snakes and Adders
Powerful Crossnumber
Magic Handkerchiefs
A Bluffer’s Guide to Symmetry
Digital Century Revisited
An Infinity of Primes
A Century In Fractions
Ah, That Explains It…
Life, Recursion and Everything
False, Not Stated, Not Proved
Proof That 2 + 2 = 4
Slicing the Doughnut
The Kissing Number
Tippe Top Twister
When Is a Knot Not Knotted?
The Origin of the Factorial Symbol
Juniper Green
Mathematical Metajoke
Beyond the Fourth Dimension
Slade’s Braid
Avoiding the Neighbours
Career Move
A Rolling Wheel Gathers No Speed
Point Placement Problem
Chess in Flatland
The Infinite Lottery
Ships That Pass…
The Largest Number is Forty-Two
A Future History of Mathematics