A construction of an ellipse, given its foci and major-axis length 2a and using a compass and straightedge, is illustrated. It is based on Dandelin's elegant proofs that the sections formed by the intersections of a cone with a plane are an ellipse, parabola, or hyperbola. (MNS)

Shows a direct solution for factoring trinomials, without trial and error, using a calculator. When a calculator is not available, the mathematical chore is eased somewhat using reference tables, as shown in two noncalculator methods (determining nonfactorability and factorability). (JN)

An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)

This paper discusses a pedagogical technique called the discovery approach in teaching remedial and college algebra. Examples of how to introduce and enhance some algebra topics using this approach in mathematics classrooms are illustrated. It is argued that student performance would improve if more topics were presented in a discovery fashion.…

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

This article traces some of the events leading up to the call for reform, differing aspects of the suggested reform, steps taken, and possible future directions for the reform of calculus instruction. (CW)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Provides four examples for testing the validity of logical arguments by using the method of truth trees. (YP)

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

Discusses the need for a geometry course in a two-year college mathematics program. Provided are guidelines for developing the geometry course separately or integrally with current curricular pattern. (25 references) (YP)

Considers the reflections of the graphs of a function through an arbitrary line. Determines whether the result is a function and which functions are reflected on to themselves through a given line. (YP)

Presents classroom curriculum and student projects that use dynamical systems--something that changes over time, such as weather or populations--to capture students' attention. (MKR)

Considered is the open-ended question of the various means of marking an n-inch ruler so that the distance of any integral number of inches from 1 to n can be ascertained with a single measurement. The relationship between a sparsely marked ruler, which is one gracefully marked with the fewest number of marks, and specific discrete graphs is…