What is Your Share of the Earthy Water and Air Resources?Harold C. Hein

Dept. of Secondary Education, The University of Mississippi,University, Mississippi 38677

Water and air have long been taken for granted since they are soabundant on the earth’s surface. Unlimited quantities of water andair have been accepted as man’s birthright. In recent years it hasbecome evident that in spite of their abundance the quantities ofwater and air that are available for man’s use are limited. The adventof space travel has promoted the concept that the planet Earth maybe thought of as a small self-contained unit or a spaceship in the vastuniverse.Answering the question, "What is your share of the earth’s water

and air resources?" provides students an opportunity to obtain neces-sary data from standard reference sources and enables students to usemathematics to obtain a quantitative answer to their questions.There will be variations in the value of the data obtained from differ-ent sources; however, a consideration of these variations will be agood learning experience.Each person’s share of the earth’s water resources was found to be

109 billion gallons (4.12X 1011!) of water. These results were obtainedusing the following data:

(1) The population of the world is 3,616,000,000 people;(2) The area of the earth covered by the oceans is 139,356,000 square miles

(3.60Xl08km2);(3) The average depth of the ocean is 12,451 feet (3.79 km);(4) 92 percent of all the water in the world is in the ocean.

This 109 billion gallons (4.12X 1011!) of water would occupy a cubeapproximately 2,440 feet (743 m) in each dimension. Continuing thisinvestigation some additional items which might be considered arethe uneven distribution of the earth’s water resources and the earth’spopulation, the water cycle, the fact that the population of the worldis increasing at the rate of 65,000,000 people per year, and the factthat the population of the world has doubled in the past 100 years.Each person’s share of the earth’s air resources was found to be

2,800,000,000 pounds (1.27X109 kg) of air and his share of oxygenwas found to be 640,000,000 pounds (2.92X 108 kg). These results wereobtained using the following additional data:

(1) The weight of the earth’s atmosphere is 5,000,000,000,000,000 tons(4.53X10^);

(2) The atmosphere is 23% oxygen by weight.

Continuing this investigation some additional items which mightbe considered are the fact that an adult requires approximately two

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pounds of oxygen a day for respiration; the carbon cycle; and therecent report that the amount of oxygen in the earth’s atmosphereseems to have remained essentially constant during the last 60 years.There are many ways in which individual teachers may wish to

modify these exercises. Some of these modifications might includeusing the metric system, emphasizing a particular mathematical skill,and emphasizing a particular scientific principle. These exericses canbe of value in helping students to develop significant concepts andthey also illustrate the interdisciplinary relationships between sci-ence and mathematics.

COMPUTER DICTIONARYSomeone has finally devised the "perfect dictionary." It has one drawback.

It’s not in alphabetical order. But no one need worry about it replacing the stan-dard a-b-c dictionary: at least not until everyone has a computer.The "perfect dictionary" is actually a computer program for arranging words

or other information in a computer memory system so that it can be easily found.It was devised last year by Prof. T. C. Hu, of the University of Wisconsin-Madi-son Mathematics Research Center and computer science department, and Dr.A. C. Tucker, now at the State University of New York at Stony Brook.The system is based on arranging items according to their probability of being

sought, rather than in alphabetical order. For Example, "the" would have topbilling in a file of English words and How-ard Hughes would rank high in a file oftop newsmakers of 1972.Hu said the method he and Tucker devised has drastically reduced the steps

needed to arrange a particular file. As computer memory banks must be updatedeach time information is added or deleted, the new technique is a great improve-ment over the two methods used previously. The new system not only takesfewer steps to arrange a new program but also requires less memory space, allow-ing more information to be stored by smaller computers.A popular method devised in 1959 requires one million steps to sort a 100 word

file. A recently devised method requires only 10,000 steps. Both, however, require10,000 memory spaces. Hu and Tuckers method requires only 700 arrangementsteps and 100 memory spaces for that size file. Hu said it took nearly a year and ahalf to develop the method."The way we do it, everything gets scrambled at first," he said, "but it comes

out all right later."