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

封面
Cambridge University Press, 1996 - 235 頁
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.
 

內容

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
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

A Hexagon in a Circle
14
Find the Rectangles
15
One Quadrilateral Begets Another
16
Five Triangles in a Pentagon
19
Number Theory
29
Algebra
33
Combinatorics and Graph Theory
37
Christmas Confusion
43
A Veritable Babel
44
ThreeDimensional Geometry 45 114 145
45
Traveling among the Pyramids
46
Connect the Dots
47
Painting a Cube
48
A Notorious Tiling Problem
73
40
94
Plane Geometry
107
No Primes Here
131
Number Theory
139
A Polynomial Fitting Problem
155
Combinatorics and Graph Theory
173
A Problem with the Elevators
182
ThreeDimensional Geometry
189
Miscellaneous
201
References
223
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