Latest page update: 1997 September 3.
Obtained from http://www.pitt.edu/~korfhage.
The exercises in this chapter may be attacked either using the Web, or not using it. (I've had a student ask me how to search without using the Web -- a sign of the times.) It is interesting to give the assignment first without the Web, then pick some of the more difficult questions for work on the Web.
1. While Donald Knuth is well known for his computer science publications, his first published work was not in that field. It was "The potrzebie system of weights and measures," in MAD Magazine, Issue #33, June 1957, pp. 36-37.
2. There is some discrepancy on the answers obtainable for this question.
Several references mention "ancient nomads" or "Persian caravan masters"
sleeping on goatskins filled with water around 3,000 years ago.
Other references suggest the ancient Egyptians.
Obviously, no specific person is credited having invented this.
Leonardo da Vinci is cited as having designed a waterbed.
There is a reference to waterbeds being mentioned in the literature in 1844.
Other references cite one of several British physicians in the
mid-nineteenth century:
3. The first problem here is to understand what joinery is. It is the art of putting wood pieces together, as in cabinet making. Once that is understood, coming up with a bibliography is not a difficult task. This question arose from an attempt to learn more about a particular kind of relatively rare dovetailing, which seemed to be in use for about ten years. That is still a more difficult question to answer, as the usual furniture and antique books do not go into that kind of detail. It took me nearly thirty years to find someone who knew the answer.
4. The answer most frequently found by students is the Tacoma Narrows Bridge, "Galloping Gertie." This, however, is not correct. The correct answer depends on what is meant by the various terms -- structure, resonance, and documentation. There are some seemingly reliable reports of bridge collapses in Britain in the eighteenth and nineteenth centuries, under circumstances that could be categorized as resonance. Much earlier than this, it is evident that the Romans knew of the phenomenon, as their legions broke step when crossing bridges. But documentation? Finally, an occasional student will suggest the walls of Jericho. Again, the question of proper documentation comes into question, along with the question of whether this really was due to resonance.
5. One student reported that he searched long and hard, but couldn't find this listed in Dissertation Abstracts. Actually, it is a humorous essay by Charles Lamb, the English author who wrote under the pen name of Elia. Apparently the idea came from a conversation that Lamb had with a friend.
6. The best source for the answer here is the litle book on the history of pi. The Indiana legislature, in the late 19th century, actually voted to assign one of several different values to pi, depending on its use. This passed the House and was on its way through the Senate when a professor from Purdue University convinced some of the legislators of the folly of the measure. It was thereupon assigned to the Committee on Swamplands, and never surfaced.
7. This is a difficult question, arising from a comment that von Neumann had
given up on this problem because it was too difficult.
One problem in hunting down the answer is that the problem has two different
names -- common set transversals, or common systems of representatives.
Apparently von Neumann never wrote anything on this problem;
at least the person who was assembling his collected works after his death
knew of no such writing.
The only reference that I have ever found is a comment toward the end of a
chapter in Paul Halmos' book on vector spaces, to the effect that von Neumann
considered the problem and felt that it seemed to present some difficulties.
This, of course, does not say whether von Neumann ever seriously worked on the
problem.
One student, however, came back with this response: "For three or more
collections of sets John von Neumann had to say that common set transversals
for them could be associated with every set by taking weak closures of
appropriate unions."
8. The best source I've found for this is KDKA, the first commercial radio station. They have a little pamphlet on the history of radio. Now K is used for stations west of the Mississippi, and W for stations to the east. However, KDKA got its license before that custom was established. I have not discovered who decided on these letters, but apparently KDKA got its call letters simply because its first transmitter was a used one from the Navy, with those letters already assigned to it according to maritime custom.
9. The obvious source of information is the local social security office. The first three letters indicate the region in which the number was issued. The next two seem to be random, and the final four are serially assigned to applicants.
10. The game is usually attributed to Sir John Suckling, an English poet of the 17th century.
11. Melongena (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) is more accurately called Solanum melongena. It is the common eggplant. Thus, while many species of Solanum are toxic, including the Deadly Nightshade, S. melongena is harmless and tasty. However, there is also a genus of mollusks named Melongena.
12. Another question on which there is conflicting information. Most references cite the well-known hockey team as the only Pittsburgh Penguins. Obviously, the hockey team would have no home runs. However, there is some indication that there was an early Pittsburgh baseball team named the Penguins. Stay tuned!
13. The custom seems to date back to an early use of a star to denote a gentlemen's facility, and a cresent moon to denote a ladies' facility. Eventually the star lost out, perhaps because of the extra labor involved in building two outhouses.
14. Again, conflicting stories abound. Joe Pye weed is one of several common
North American herbaceous weeds with medicinal properties.
The name is usually applied to Eupatorium purpureum, but has also been
given to E. dubium, E. fistulosum, E. maculatum, and possibly other species
of Eupatorium.
The most common story is that Joe Pye was an American Indian medicine man who
used the herb to help early New England colonists cure typhus or typhoid and
other fevers.
Another story is that the name is actually a corruption of an American Indian
word, jopi, for typhoid fever.
Other references to the name that have been found include the following:
15. This is attributed to Abraham Lincoln.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. Since there are ten characters in Example 2.1, four bits are necessary in a flat code. The Huffman code requires an average of 227/98, or approximately 2.316 bits per character.
11.
12. The character string aaaa... encodes as 0110011001100110... If decoding begins wrongly with the third bit, the string is decoded as dddd....
13. For aaa, the initial a is in the interval 0.000... to 0.333.... The second a puts the code in the interval 0.000... to 0.1666.... Finally, the third a puts the code in the interval 0.000... to 0.1000....
14. Since the value is less than 0.333... the first letter is a. Since the value is greater than 0.1666... and less than 0.25... the second letter is b. At this point the perceived frequency is a: 2, b: 2, c: 1. Thus since the value is between 0.1666... and 0.19000... the third letter is a. Hence the code can represent aba. If there is a fourth character in the string, it will similarly be found to be a.
15.
16.
1. The number of combinations of four out of seven terms is C(7,4) = 35.
2. The expression A OR (B AND C) will retrieve everything involving A and also documents containing B and C but not A. The expression (A OR B) AND C will only retrieve documents that contain C and (either A or B or both).
3.
4. The expression (A AND B) OR (A AND C) retrieves documents that contain A and (either B or C or both). The expression (A OR B) AND (A OR C) retrieves these, and also documents containing A but neither B nor C, and documents containing both B and C but not A.
5.
6.
1. For n = 1 the slope is -logeb; for any larger value of n the slope is 0.
2.
3.
4.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
1.
2.
3.
4.
5.
6.
7.
8.
9.
1.
2.
3.
1.
2.
3.
4.
5.
6.