Uses the context of rock climbing to discuss the science concept of friction. Presents the mathematics equations that describe the concept. Examines the physics of different rock climbing situations encountered and equipment used. A series of related problems with answers is provided. (MDH)

Explores applications of the Fibonacci series in the areas of probability, geometry, measurement, architecture, matrix algebra, and nature. (MDH)

Utilizes the problem of determining the number of different ice cream cones and cups that can be made from a choice of 31 flavors to investigate the concepts of combinations and permutations. Provides a set of six related problems with their answers. (MDH)

Discusses the energy flux-density of two beams of light of equal energy that are intersected at a given angle. Examines an apparent contradiction to the physics law of conservation of energy known as Vavilov's paradox. (MDH)

Discusses flexible polyhedrons, called flexors, that can be bent so that the faces stay rigid while the angles between them seem to change. Presents models representing flexors and directions on how examples can be constructed. (MDH)

Cultivates a definition for the surface area of a sphere with successive approaches. The first utilizes the notion that a sphere cannot be "developed" in the mathematical sense that a cylinder can be cut, unrolled, and measured. The second considers approximations by polyhedra. The third uses Minkowski's definition to introduce the…

Presents a series of challenges, problems, and examples to demonstrate the principle of mathematical induction and illustrate the many situations to which it can be applied. Applications relate to Fibonacci sequences, graph theory, and functions. (MDH)

Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

Presents six learning activities dealing with planetary motion, the launching of satellites, and Halley's comet, all of which utilize the three laws of Johannes Kepler. These three laws are discussed in detail, and answers to the activities are provided. (KR)

Presents illustrated examples that promote problem solving through the student's consideration of a visible predicament from a three-dimensional viewpoint rather than the typical planar perspective. Includes six student exercises involving rays, circles, quadrilaterals, and hexagons, with hints and solutions provided. (JJK)

Describes differences in the composition, pressure, and temperature at distinct altitudes of the Earth's atmosphere from the point of view of physical laws. Discusses the genesis and importance of ozone, thermal radiation and the "layer cake" arrangement of the atmosphere, and solar energy in connection with thermal equilibrium. (JJK)

Describes the Mathematics Correspondence School that was organized in late 1960s and still directed by the author, to serve about 1,000 Russian secondary students in small cities and remote villages. Discusses this project's extension to other disciplines, and the introduction of English versions of the school's textbooks via this regular journal…

Presents six learning exercises that introduce students to the mathematics used to control and track spacecraft attitude. Describes the geocentric system used for Earthbound location and navigation, the celestial sphere, the spacecraft-based celestial system, time-dependent angles, observer-fixed coordinate axes, and spacecraft rotational axes.…

Describes the use of analogy relative to the classical theory of momentum and kinetic energy, and addresses the advantages and disadvantages of this approach with respect to modern physics. Discusses the origins of the billiard ball analogy in the work of Coriolis and its influence on later theories and investigations of nuclear fission, particle…