Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

While it is most often the case that an understanding of physics can simplify mathematical calculations, occasionally mathematical precision leads directly to a better physical understanding of a situation. Presents an example of a mechanics problem in which careful mathematical derivation can lead directly to a deeper physical understanding of…

Presented is a method for factoring quadratic equations that helps the teacher demonstrate how to eliminate guessing through establishment of the connection between multiplication and factoring. Included are examples that allow the student to understand the link between the algebraic and the pictorial representations of quadratic equations. (JJK)

Presents simple experiments using the flow of water from bell jars that can provide an easily visualized introduction to exponential decay. (Author)

Discusses a misconception about the cycloid that asserts the final point on the path of shortest time in the "Brachistochrone" problem is at the lowest point on the cycloid. Uses a BASIC program for Newton's method to determine the correct least-time cycloid. (MDH)

This section provides mathematical activities in reproducible formats appropriate for students in grades 8-10. The activity is designed to provide an experience in model building while developing the concept of slope. (PK)

Described is a graduate level engineering course on functional analysis offered at Purdue University. The course restricts itself to linear problems, specifically analysis of linear operators on vector spaces. Key applications in the course demonstrating the utility of abstract formulations are presented. (BT)

Presents a motion problem that students in a college physics class are asked to solve and later asked to continue to analyze until they have stopped learning from the problem or the problem itself is finished. (MDH)

A major cause of the difficulty undergraduate mathematics majors have with the transition from elementary to advanced mathematics courses is that advanced courses require students to understand how mathematics is created. Describes a course whose main purpose is to introduce students to the creative process in mathematics. The course consists of…

Discusses three types of bridges to determine how best to model each one: (1) drawbridge; (2) balance bridge; and (3) bascule bridge. Describes four experiments with assumptions, analyses, interpretations, and validations. Provides several diagrams and pictures of the bridges, and typical data. (YP)

Presents two methods of calculating the expected value for a participant on the television game show "The Wheel of Fortune." The first approach involves the use of basic expected-value principles. The second approach uses those principles in addition to infinite geometric series. (MDH)

Emphasizes a real-world-problem situation using sine law and cosine law. Angles of elevation from two tracking stations located in the plane of the equator determine height of a satellite. Calculators or computers can be used. (LDR)

Explores the problem of combining algebraic terms from the students' point of view and suggests changes in certain traditional teaching practices. (PK)

Presents a problem to determine conditions under which two identical masses, constrained to move along two perpendicular wires, would collide when positioned on the wires and released with no initial velocity. Offers a solution that utilizes the position of the center of mass and a computer simulation of the phenomenon. (MDH)

Describes software, hardware, and devices that were designed to provide students with an environment to experiment with basic ideas of mechanics, including nonlinear dynamics. Examines the behavior of a Lorenzian water wheel by comparing experimental data with theoretical results obtained from computer-based sensors. (MDH)