Contents for September 2000
The problem is to determine where an object is by taking sightings from several sites. The difficulty is that the position determined is not a point but an area. If we must report a point, which do we choose and how do we find it?
The Lognormal Distribution
Brian E. Smith and Francis Merceret
The lognormal distribution is all around us: incubation period of diseases, duration of employment, time to divorce, lengths of telephone calls. Its properties should be better known. If you assume (wrongly, but people do) that wind velocities are normally distributed, you are going to underestimate badly the probability that a space shuttle launch will have to be postponed.
Can We Improve the Teaching of Calculus?
The author says, "We not only can; we should. The usual treatment is illogical." Will we eliminate the illogicality? Probably not. But it does no harm, and may do some good, to look closely at what we tell innocent students.
Food and Drug Interaction: What Role Does Statistics Play?
When should you take that pill: before dinner, in the middle of it, after it, or long after it? It depends on the pill, of course, but the question needs to be answered. Samples must be drawn, doses given at various times, concentrations of drugs in the blood measured, and statistics applied to find out what is best.
Some New Results on Magic Hexagrams
Let us construct a regular six-pointed star and divide the interior hexagon into six triangles. How can we place the integers from 1 to 12 in the twelve triangles to get the same sum in all the rows of five numbers, and what can the magic sum be? If your answer is "Who cares?" then shame on you. Martin Gardner cares, considers several related questions, and ends with an exercise for the reader.
The Calculus and Gamow's Theory of Gravitation
D. A. Linwood
Gravity is mysterious. George Gamow once proposed explaining it by assuming the existence of particles, an enormous number of them, found everywhere in space and moving at random, that are slowed up a little bit when they pass through a mass. The explanation works! Dr. Linwood shows how Newton's Law of Gravitation follows, easily, from Gamow's assumption.
Colin Maclaurin's Quaint Word Problems
Word problems we have always had with us. The Rhind Papyrus (c. 1650 b.c.) is full of them and so are textbooks today. Colin Maclaurin couldn't get along without them either. "A man and his wife usually drink a keg of beer in 12 days. They found by often experience that when his wife was absent the man drank it in 20 days. In how many days will the wife alone drink it?" Thus is mathematics learned, and thus it shall always be learned.
The Orbits of a Unimodular Affine Transformation
Roman W. Wong
Take a point, see where a linear transformation takes it, see where the new point goes, and continue. Sometimes you get a spiral, sometimes an ellipse, every now and then points on a y = , other times something else. Professor Wong shows how we can tell, in some cases, what is going to happen.
Collapsed Matrices with (Almost) the Same Eigenstuff
Small matrices are more friendly than large ones. Professor Hooley shows how to replace a big matrix with a littler one without losing very much information about the big one's eigenvalues.
Applications of Fourier Series in Classical Guitar Technique
You probably didn't know that guitarists can play sol tasto or sol ponticello. Well, they can, and the sounds are different. There is a simple mathematical explanation.
Fast-food-frustra and the Center of Gravity
An important question: when is your drink, whether regular or super-sized, least likely to tip over in your cup holder? This Capsule may change your drinking habits forever! Then again, it may not, but the answer is appealing.
Fallacies, Flaws, and Flimflam
Two numerical analysis texts, one in its second edition and the other in its third, contain the same false statement. Use them at your own risk!
Student Research Project
A Project for Discovery, Extension, and Generalization in Abstract Algebra
Review of StudyWorks by Pat Stone.
Problems and Solutions