The development of calculus and science by being permanent, didactic, demands on one part an analytical, deductive study and on another an application of methods, rhochrematics, resources, within calculus, which allows to dialectically conform knowledge in its different phases and to test the results. For the purpose of this study, the motivation…

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

Presents a mathematics problem involving speed of a walking student versus speed of light reflection in a high school hallway. (MKR)

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

The article presents and discusses an optimization problem concerned with observing objects from a moving car. (MK)

Describes a project in which trigonometry and precalculus students cooperate to measure the height of an inaccessible water tower. (MKR)

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)

Considered are the main elements of computational chemistry problems and how these elements can be used to formulate the problems mathematically. Techniques that are useful in devising an appropriate solution are also considered. (Author/TG)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

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)

Presented are five short articles which describe innovations in mathematics teaching. Included are "Polar Summation,""The Age of the Solar System,""Forward Homework--A Motivational Tool,""Trigonometric Identities through Calculus," and "Algorithms for Evaluation of Polynomials." (CW)

Discusses two teaching ideas: (1) copying and distributing anonymous student mathematics homework to the class to increase student responsibility and their ability to communicate and read mathematics, and (2) using maximum/minimum applications of calculus to investigate the most economical dimensions for manufactured metal cans. (MKR)

This discussion deals with the question, are there integral rectangles such that a box of maximum volume is obtained by removing an integral-sided square from each corner? An equation to solve the problem is generated and a table of values presented. The material appears suitable for beginning calculus students. (MP)

Various methods for solving the problem of finding when the hour and minute hand of a watch have the same direction are explored. The relationship of these problems to the educational environment and the maturity of the student are discussed. (CW)