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 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…