Harris S. Schultz and Ray C. Shiflett
Consider a sequence recursively formed as follows: Start with three real numbers, and then when k are known, let the (k +1)st be such that the mean of all k +1 equals the median of the first k. The authors conjecture that every such sequence eventually becomes stable. This article presents results related to their conjecture.
If Is Constant, Must f (t ) = c / t ?
Tian-Xiao He, Zachariah Sinkala, and Xiaoya Zha
The familiar property of integral of led to the discovery of other functions with this property.
Intersections of Tangent Lines of Exponential Functions
Timothy G. Feeman and Osvaldo Marrero
This article looks at how a particular curve associated with tangents of an exponential function is a copy of the exponential itself.
The Probability that an Amazing Card Trick Is Dull
The author describes a card trick that failed when he tried it with the student chapter at his university. Computations show that the chance of this happening is about 1 in 25.
Making a Bed
Anthony Wexler and Sherman Stein
The origins of this paper lay in making beds by putting pieces of plywood on a frame: If beds need to be 4 feet 6 inches by 6 feet 3 inches, and plywood comes in 4-foot by 8-foot sheets, how should one cut the plywood to minimize waste (and have stable beds)? The problem is of course generalized.
A Geometric Series from Tennis
In this note, a formula is found, using geometric series, for the probability that a player wins from deuce (by the required two points) given a fixed probability p of winning each point.
On Sums of Cubes
Hajrudin Fejzic, Dan Rinne, and Bob Stein
The sums of cubes discussed here are modifications of the well known identity
Symmetry at Infinity
The symmetry in the title arises in the centers of masses of some plane laminas.
The Flip-Side of a Lagrange Multiplier Problem
Angelo Segalla and Saleem Watson
The “flip-side” of an optimization problem is dual in the way that maximizing the area of a rectangle with given perimeter corresponds to minimizing the perimeter for fixed area. This note looks at this duality from a Lagrange multiplier perspective.
Another Proof for the p-Series Test
Yang Hansheng and Bin Lu
The proof presented here is an alternative to the integral test that is usually used.