A Divertimento on the Symbols of the Elements Boyd L. Earl University of Nevada, Las Vegas, Las Vegas, NV 89154
The following exercises provided some amusement in their devising. I hope that they will do likewise for the reader, and that they may stimulate some interesting approaches to teaching the symbols of the elements. First Movement
People who like word games occasionally undertake the construction of crossword squares; e.g., CARE ORES REAP NARY One can form such squares with the symbols of the elements, where the dimension is, of course, restricted to 2 x 2, and capitalization is ignored. Simple squares are easy to find:
In these. the svmbols are read in the usual directions. One can make the exercise more challenging by looking for sauares in which both diaeonals. read from top to bottom, are also symbols: NP BA
AC LU
Such squares contain at least six two-letter symbols. The "ultimate challenge'' is to find squares in which the reverse directions also read as symbols. The square on the right above, for example, contains La, reading bottom to top, and Ca, reading right to left. (It's more difficult to find squares containing only six symbols, with none in the reverse directions.) If one includes the diagonals read from bottom to
top, the number of two-letter combinations is 12. It is impossible to construct a square with 12 symbols. I believe the maximum is nine, as in CA RS How many more distinct nine-symbol squares can you find? Since we read in all possible directions, any two squares with the same four letters are not distinct; they contain the same symbols. Second Movement How many elements can you identify whose symbols match the officialtwo-letter abbreviationsfor the names of states, ignoring capitalization conventions? Third Movement The following paragraph is composed according to a rnle. First discern the rule. Then see if you can compose a longer paragraph according to the same rule. (The next section may give away the solution to the first item.) One thing a person can be sure of is that when he takes a rest another person can step in and assert his position over that ofthe rester and, ifheis not mindfulinhis repose, pose what can be a serious threat. One resolution is no resting-a poor answer. Otherwise, one can constantly scan the scene for any potential threat, being ever prepared, you can be sure, for an appropriate response, if necessary. Coda What is the longest single English word which is a succession of chemical symbols (e.g., salaries). I have found a word of 16 letters. (Answerson page 1022)
Volume 68 Number 12 December 1991
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, with vivid photographs illustrating that "doing science" can be much more rewarding than reading a text or listening to a lecture. Also, teachers learn current scientific information about the environment that can be difficult to obtain. Moreover, college undergraduates relate well to high school students because the age difference between them is small. High school students often ask questions about college life that the undergraduate can answer from personal experience. This year we have branched out and are speaking at junior high and middle schools. This program also benefits the undergraduate speaker in many ways. First, college undergraduates learn the science behind pressing environmental concerns. Second, it gives students many hours ofspeaking experience, which is often lacking in traditional science and engineering degree requirements. Third, the program provides an opportunity to meet university faculty members and other interested students in an infonnal, educational setting. Finally, such a the program builds self confidence and leadership skills. Some secondary school teachers may have the opportunity to bring in scientists to describe careers to their students. But searching for such speakers can be time-consuming and may be impossible for those in rural areas. A
well-organized and sufficiently funded university outreach program can serve the needs of even the most rural schools at little cost. Several of our undergraduates traveled to Eastern Washington during their spring break to speak at high schools that were still in session. '!\vo speakers gave 14 talks at nine rural high schools in three days! To make a significant impact on impending shortages of scientists, similar science outreach programs must be organized at other university centers across the country. We are willing to consult and help in any way we can. To date over 50 other universities in the United States and several foreign countries have expressed interest in starting their own programs. We feel that each university will develop a unique program that matches the experience and skills of the available faculty. Our hope is that a string of universities will develop similar programs to enhan~e high school curricula through undergraduate presentations. Acknowledgment
The authors thank Sara Selfe, G. Gorden, D. J. Woodman, G. Christian, M. Gouterman, and Robin Ryan for their helpful criticism of this article.
Answers to the "Divertimento" on page 1011 First Movement I have identified three other nine-symbol squares:
CS RE
CL AR
SB ER
The order in which the letters are placed into the square is immaterial. With the given orders, one obtains six symbols read in the left-to-right and top-to-bottom directions. I have also fOWld 15 eight-symbol squares.
Second Movement AI, AI, Ca, Co, Ga, In, La, Md, Mn, Mo, Ne, Nd, Pa, and Sc are the 14 symbols.
Third Movement The rule is that the entire paragraph is a sequence of symbols for the elements. Capitalization is disregarded, of course, and a two-letter symbol may be split between words. The explicit analysis into symbols is given for the first line:
OINe! ThlIn/G aJ PlEr/SiOIN/ CaIN/ Be! SlUIRe! OIF/ lISi ThlAt/ W/He/N/ He! TalKIEs...
Coda "Superciliousness" has 16 letters.
1022
Journal of Chemical Education
