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