# Is Mathematics all around us?

1. The Grand Canyon in Arizona is 217 miles long, ranges in width between 4 and 18 miles, and is up to 1 mile deep. If we conservatively take its average width to be 6 miles and its average depth to be .3 mile, then its volume is 390.6 cubic miles, which, upon multiplication by 5,2803, yields 5.75 x 1013 cubic feet. If we divide this figure by 5 billion, the human population of the earth, we come up with approximately 11,500 cubic feet of space in the Grand Canyon for every human being on earth. Calculating the cube root of this figure to be about 22.5 feet, the conclusion is that there would be room in the Grand Tenement for 5 billion cubicle apartments 22.5 feet on a side.

J. A. Paulos, Beyond Numeracy
Vintage Books, 1992

2. Suppose we want to know the average income of the employees of the Brand X Corporation. Here's the accounting of salaries:

 \$470,000 President \$100,000 President's wife \$80,000 Each of the wife's three brothers \$50,000 Wife's best friend from high school \$30,000 Plant manager \$25,000 Each of the six production workers

They must whistle while they work! The average employee of the Brand X Corporation earns \$80,000! (The total annual payroll of \$1,040,000 divided by thirteen employees equals \$80,000.) The president's wife can truthfully say that her brothers earn no more than the average employee. And think of how happy everyone will be if the president earns \$990,000 next year. (The total annual payroll of \$1,560,000 divided by 13 will equal \$120,000.) And the president's wife could now truthfully say that she earns less than the average employee.

Marylin vos Savant
The Power of Logical Thinking
ST. Martin's Press, NY, 1996

3. The time in which any space is traversed by a body starting from rest and uniformly accelerated is equal to the time in which that same space would be traversed by the same body moving at a uniform speed whose value is the mean of the highest speed and the speed just before acceleration began.

Galileo Galilei
Dialogues Concerning Two New Sciences, 1636

4. The next Observation is, That there be more Males than Females. There have been Buried from the year 1628, to the year 1662, exclusive, 209436 Males, and but 190474 Females; but it will be objected, that in London it may indeed be so, though otherwise elsewhere; because London is the great Stage and Shop of business, wherein the Masculine Sex bears the greatest part. But the Answer, That there have been also Christened within the same time, 139782 Males, and but 130866 Females, and that the Country Accompts are consonant enough to those of London upon this matter.

J. Graunt
Foundations of Vital Statistics
London, 1662

5. I (and at least one other person, J. Adam - professor of mathematics at the Old Dominion University) believe that this is a common perception that the shadow thrown by a person moving away from a street light grows at an increasing rate. Do you agree with that? Give it a thouhgt and then check the answer on a separate page.