Presents a brief historical sketch of the life and work of one of the founders of modern mathematical physics. Discusses three problem-solving applications of the Poisson distribution with examples from elementary probability theory. Provides background on two of his noteworthy results from the physics of oscillations and the deformation of rigid…

Discusses how early notions about celestial mechanics were restructured, one by one, involving the following concepts: the celestial sphere and its rotation; the spherical earth; planetary motion; and models for the solar system initiated by Eudoxus, Hipparchus, Ptolemy, and Copernicus. (JJK)

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)

Discusses the hydrodynamic reasons why a riverbed meanders through a plain. Describes how water movement at a bend in a river causes erosion and changes in the riverbed. Provides a mathematical model to explain the periodic shape of meanders of a river in a plain. (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)

Traces cosmogonic history of solar system from Laplace's hypothesis of revolving gas nebulae, to Newton's two-body problem with its mathematical impossibility of gravitational capture, to the isosceles three-body problem of Schmidt and Sitnikov with its notion of partial capture, and finally to the total capture model of Alexeyev verified by the…

Describes the great variety of observations surrounding the auroras (both borealis and australis), and provides photographs from the space shuttle, Discovery. Discusses where and when the auroras can be observed, the process that the Earth's magnetic phenomena fulfill in how and why auroras appear, and the effects of solar wind upon auroras. (JJK)

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)

Reprinted from the original Russian manuscript of Yakov Zeldovich, this article chronicles his studies of the universe and his attempts to construct a theory of its evolution. He provides the high school student with compelling cosmological discussions about uniformity, galactic clusters, radiation, evolution, the big bang, and gravitational…

Presents basic facts about quasars as most powerful sources of radiation in the universe. Describes in detail the mirages and illusions that quasars generate and methods for their interpretation. Includes the notion of the gravitational lens and its relationship to twin quasars and the apparent measure of a quasar's bright jet tail moving faster…

Describes the genesis, the early experiments, and the limitations of X-ray astronomy. Discusses original methods for searching and locating the first interstellar X-ray source, modern attempts to identify a massive black hole as part of a binary system X-ray source, and the effort to generate X-ray images of solar flares. (JJK)

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)