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.

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

It is usually assumed that successful problem solving in knowledge-rich domains depends on the availability of abstract problem-type schemas whose acquisition can be supported by presenting students with worked examples. Conventionally designed worked examples often focus on information that is related to the main components of problem-type…

The aim of this paper is to evaluate the use of trace diagrams for analysing collaborative problem solving. The paper describes a study where trace diagrams were used to analyse joint navigation in a virtual environment. Ten pairs of undergraduates worked together on a distributed virtual task to collect five flowers using two bees with each…

Hadamard's two integral inequalities are generalized and the quadrature formulae associated with them are demonstrated.

Several ways for solving inequalities have been suggested in the literature, among them graphical, verbal and algebraic solutions. A new look at solving inequalities via use of the intermediate value theorem is presented here, and this method may prove to be straightforward for many students.

In this note, the author considers a class of infinite series and shows that these are equivalent to a number of definite integrals, some of which are improper integrals. By using Taylor's theorem in this equivalence the author establishes convergence of each series, and a means of evaluating the sum of the series and the definite integral to any…

Solving problems often means trying out ideas one knows about which might lead down blind alleys. In this article, the author provides a solution to the following simple mathematical problem: Suppose you have four points which are on the four sides of a square, how do you construct the square? He says that the obvious place to tackle it is to use…

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

This article describes the connection between a novel puzzle and uses of algebra to generalize the fewest moves to solve it.

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

We tested the hypothesis that peer instruction enhances student performance on qualitative problem-solving questions. To test this hypothesis, qualitative problems were included in a peer instruction format during our Physiology course. Each class of 90 min was divided into four to six short segments of 15 to 20 min each. Each short segment was…

An explicit formula is established for the general solution of the homogeneous non-autonomous linear difference equation. The formula developed is then used to characterize globally periodic linear difference equations with constant coefficients.