E-Book Overview
Sink or Float: Thought Problems in Math and Physics is a collection of problems drawn from mathematics and the real world. Its multiple-choice format forces the reader to become actively involved in deciding upon the answer. The book s aim is to show just how much can be learned by using everyday common sense. The problems are all concrete and understandable by nearly anyone, meaning that not only will students become caught up in some of the questions, but professional mathematicians, too, will easily get hooked. The more than 250 questions cover a wide swath of classical math and physics. Each problem s solution, with explanation, appears in the answer section at the end of the book.
A notable feature is the generous sprinkling of boxes appearing throughout the text. These contain historical asides or little-known facts. The problems themselves can easily turn into serious debate-starters, and the book will find a natural home in the classroom.
E-Book Content
The Dolciani Ma thematical Expositions NUMBER THIRTY-THREE
Sink or Float? Thought Problems in Math and Physics
Keith Kendig Cleveland Slale Univer:sily
Published and DistribUied by The Mathematical Association of America
What Do You Think? A Sampler Cube-Shaped Fishing Weight A metal cube is suspended by a vertex to make a tishing weight:
be is slowly \he CU d into the lowere water.
The shape of the water line on the cube changes as the cube dips into the water.
The weight is lowered into a quiet pond until it is half submerged_ What is the shape of the waterl ine on the cube's surface? (a) Triangle
(b) Square
(d) Hexagon
(e) Octagon
( c) Non-square rectangle
(p.2 17)
1
Sink or FI_? Thought Problems in Math and Physics
2
Subtracting by Adding? This illustration shows three subtraction problems changing into addition problems. In the first step. the number being subtracted is replaced by its digitwise nines complement. For example, the nines complement of 3 is 6, because 6 completes 3 to make the sum 9. Does the method suggested by these examples generalize? Could all that time grade-school kids spend learning borrowing be eliminated?
62 - 17
•
62 + R2 144 'J
305 -92
•
•
45
•
213
305 + 07 312 'J
2876 - 321
•
2876 + 678
3554
2555
_______'-J
Here, 1 is transferred from the leading digit to the last digit to get the final result.
Can one always use the method suggested in the picture to subtract a smaller positive integer from a larger one? (a) These special examples work, but there is no general free lunch here. (b) Usually yes, but there are except ions that cou ld easi ly lead to confusion for the kids. (c) Yes for integers. but the method doesn't work for decimals. For these, they would sti ll need the traditional method. (d) It always works.
(p.2 17)
3
A Sampler
Would This Tempt You? You have just wo n $100,000 on a qui z show. You no sooner begin to recover from the shock than the emcee offers you a deal. The curtain behind you opens, revea ling two baskets with 50 ping-pong ba lls in each. The only difference between them is that in one basket the balls are red, whil e in the other they are yell ow. He says you can mix them up or transfer any number of them from e ither basket to the other. But once you have done that, you are blindfolded, the contents of each basket are stirred, and the baskets are moved around. You then randomly choose a basket and take out a ping-pong ba ll .
50 yellow ...
... and 50 red balls
Can you increase your chances of winning by rearranging the ping-pong balls?
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