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
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
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.
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
How to lead a class to discover Gaussian quadrature in a natural way.
Multiplying and Dividing Polynomials Using Geloxia
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.