Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries

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Cambridge University Press, 1996 - Education - 235 pages
3 Reviews
This book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. This collection will give students, teachers, and university professors a chance to experience the pleasure of wrestling with some beautiful problems of elementary mathematics. Readers can compare their sleuthing talents with those of Sherlock Holmes, who made a bad mistake regarding the first problem in the collection: Determine the direction of travel of a bicycle that has left its tracks in a patch of mud. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. For example, if a pizza is sliced into eight 45-degree wedges meeting at a point other than the center of the pizza, and two people eat alternating wedges, will they get equal amounts of pizza? Or: Is an advertiser's claim that a certain unusual combination lock allows thousands of combinations justified? Complete solutions to the 191 problems are included with problem variations and topics for investigation.
 

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Very interesting, many further informations and generalisations are provided.

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a perfect investigation book.

Contents

Plane Geometry
1
Nested Triangles
7
How Many Isosceles Triangles?
8
Triangles from a Triangle
9
Circular Surprises
10
A Ring of Disks
11
If You Lose Your Compass
12
An Ellipse and a Circle
13
The Color of Money
38
Cover the Honeycomb
39
Decimal Diversity
40
Breaking Up Space
41
Count the Tilings
42
Difference Triangles
43
A Veritable Babel
44
ThreeDimensional Geometry
45

A Hexagon in a Circle
14
Find the Rectangles
15
One Quadrilateral Begets Another
16
A Constant Difference
17
Another Area Comparison
18
A Hexagon of Centroids
19
A Short Bisector
20
Miscellaneous 64 Nearest Neighbors
21
Whats the Angle?
22
A Shady Garden Wall
23
Number Theory
25
Theyre There but Where?
26
Reversing Multiples
27
A Very Good Year
28
A Sum of Fractions
29
Theyre in the Money
30
A Necessary Square?
31
Sums and Differences
32
Algebra
33
Powerful Patterns
34
Playing the Stock Market
35
A Shuffling Reconstruction
36
Combinatorics and Graph Theory
37
Traveling among the Pyramids
46
Connect the Dots
47
Painting a Cube
48
Surveying on Earth
49
Miscellaneous
51
A Complicated Constant
52
An EggDrop Experiment
53
A Messy Desk
54
Throw Your Rings into the Hat
55
Passion Has No Square Root
56
Catch the Counterfeit
57
Divide and Be Conquered
58
An Odd Vector Sum
59
How Many 8s Can a Plane Hold?
60
Plane Geometry
63
Number Theory
131
Algebra
155
Combinatorics and Graph Theory
165
ThreeDimensional Geometry
189
Miscellaneous
201
References
223
Index
233
Copyright

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About the author (1996)

Stan Wagon is a Professor of Mathematics at Macalester College, Minnesota. He is a winner of the Wolfram Research Innovator Award, as well as numerous writing awards including the Ford, Evans, and Allendoerfer Awards. His previous work includes A Course in Computational Number Theory (2000), The SIAM 100-Digit Challenge (2004), and Mathematica(r) in Action, 3rd edition (2010).

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