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By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

An elementary analysis of a common textbook airplane problem is given, and then, as an illustrative example, the possibilities of this mechanism for animal navigation are briefly considered. (Author/MA)

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)

Presents the theory of primary and secondary rainbow formation utilizing simple optics and geometric concepts. Describes an appropriate, waterless classroom demonstration and includes the relevant mathematical formulas and models. (JJK)

A model of Brownian motion is discussed which includes viscosity effects. The model lends itself to Monte Carlo simulation and thus is suitable for an elementary physics laboratory experiment. (BB)

Addresses the problem that students balk at the notion velocities do not add algebraically. Offers a geometric model to verify the algebraic formulas that calculate velocity addition. Representations include Galilean relativity, Einstein's composition of velocities, and the inverse velocity transformation. (MDH)

Uses the problem of determining when a car and truck traveling at the same speed will collide after the truck has applied its brakes to illustrate the need to consider boundary conditions when solving problems in elementary mechanics. (MDH)

Identifies and discusses the overlap between mathematics and physics at different educational levels. Presents some examples of the overlap and some suggestions for teachers. (YP)

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)

Criticizes the current method of formalization in Italian schools and the use of tools of the mathematical method. Proposes a general three-stage formalization method which can used for physical quantities, the particular significance of certain quantities, and the description and interpretation of phenomena. (TW)

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 the deterministic simulation (a given input always leads to the same output) and probabilistic simulation (new states are subject to predefined laws of chance). Provides examples of the application of the two simulations with mathematical expressions and PASCAL program. Lists seven references. (YP)

Discusses the global change of climate. Presents the trend of climate change with graphs. Describes mathematical climate models including expressions for the interacting components of the ocean-atmosphere system and equations representing the basic physical laws governing their behavior. Provides three possible responses on the change. (YP)

Presents the origin and mathematics of Hubble's Law of the expanding universe. Discusses limitations to this law and the related concepts of standard candles, elliptical galaxies, and streaming motions, which are conspicuous deviations from the law. The third of three models proposed as explanations for streaming motions is designated: The Great…