The College Mathematics Journal - January 1999

Articles

Coming to America: The Journey of an Immigrant Scholar
Clifford H. Wagner

An interview with Vedula N. Murty, Professor Emeritus of Mathematics and Statistics at the Pennsylvania State University, covering his early life and education in India and his professional life in (and outside of) the United States.

The Asymmetric Propeller
Martin Gardner

A theorem, seventy years old at least and of unknown origin, says that if three congruent equilateral triangles are have corners meeting, the midpoints of the lines joining the other two vertices of the triangles are vertices of an equilateral triangle. The late Leon Bankoff discovered that the triangles don't have be congruent and don't have to meet at a point. Martin Gardner describes the results, and conjectures that the triangles don't have to be triangular--squares seem to work as well.

 

Spirals and Conchospirals in the Flight of Insects
Khristo N. Boyadzhiev

A model of insect flight explaining why insects that are attracted to a light spiral toward it. This holds only for nearby lights: if an insect is attracted by the moon, it will fly toward it in a straight line.

Student's t and Crackers
Paul M. Sommers

Are the contents of boxes of animal crackers randomly distributed? No! There are too many rhinoceroses and not enough bears. Further, boxes do not contain enough crackers.

Gabriel's Wedding Cake
Julian F. Fleron

Gabriel's horn is the well-known solid with finite volume and infinite surface area that is generated by rotating y = 1/x around the x-axis. Gabriel's wedding cake is another solid with the same properties, which can be demonstrated without using calculus.

Classroom Capsules

Maximizing the Arclength in the Cannonball Problem
Ze-Li Dou and Susan G. Staples
Everyone knows to point a cannon at a 45 degree angle to maximize the range of a cannonball, but until you read this you will not know at what angle to point it to make the ball travel a maximum distance through the air. (Through the vacuum, actually, since air resistance is neglected.)

Pictures Suggest How to Improve Elementary Numerical Integration
Keith Kendig
How to lead a class to discover Gaussian quadrature in a natural way.

Multiplying and Dividing Polynomials Using Geloxia
Jeff Suzuki
Long ago, numbers were multiplied by using a grid. Polynomials can be multiplied in the same way. They can also be divided using the same grid, illustrating what is not obvious with the usual algorithms, that multiplication and division of polynomials are inverse operations.

Software Review

Cyclone, the Implicit 3D Plotter
Reviewed by Jon Wilkin
Cyclone is a three-dimensional graphing package with many valuable features.

Book Review

Women in Mathematics
by Claudia Henrion,
Reviewed by Anita Solow

Filler Material

A proof that the set of upside-down A's has the same cardinality as the set of backwards E's, a zero-free square triangular number, a joke about calculus books, and other items.