A very common Applied Optimization Problem in Calculus deals with minimizing a distance given certain constraints, using Calculus, the general method for solving these problems is to find a function formula for the distance that we need to minimize, take the derivative of the distance function, set it equal to zero, and solve for the input value,…

By describing the motion of a charged particle in the well-known nonuniform field of a current-carrying long straight wire, a variety of teaching/learning opportunities are described: 1) Brief review of a standard problem; 2) Vector analysis; 3) Dimensionless variables; 4) Coupled differential equations; 5) Numerical solutions.

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

The author uses Stella the Spider as the main character in a number of three-dimensional geometry problems. Eight of these problems are discussed, with solutions. (MNS)

A problem-solving approach involving systematic experimentation, one of the most-used problem-solving strategies, is advocated since it is useful beyond mathematics problems. Examples of its use are given, with two problems explored and four others noted. (MNS)

Comments on student responses to the three dimensional items produced by first investigating flat paper cutouts of the items. (KHR)

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

Five basic skill areas needing more attention in standard high school geometry are discussed. Levels of student mental development in geometry and a need for less emphasis on formal proofs are reviewed. (MP)

Presents 14 distinct methods to determine the sine of the angle formed by the line segments joining one vertex of a square to the midpoints of the nonadjacent sides. Nine methods were developed by mathematics club participants preparing for mathematics competitions and the remaining five by faculty members. (MDH)

Presents two ancient problems, trisecting any angle and dividing a circle into any number of equal parts. Illustrates how to use these problems to prompt students to think broadly and creatively about problems instead of letting the apparent boundaries of the problem limit their thoughts. Combines three-dimensional solutions to the problems to…

Shows that the ratio of the area of the quadrilateral formed by joining the kth points to the area of the original quadrilateral is constant whether it is convex or concave quadrilateral. Presents many geoboard or dot paper diagrams and geometrical expresssions. (YP)

The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)