This paper deals with a brief history of the most remarkable Euler numbers "e,"?"i"?and?"?" in mathematical sciences. Included are many properties of the constants "e,"?"i"?and?"?" and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special…

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

A 100 years-old formula that was given by J. J. Thomson recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson and later published by Pappas. Unfortunately, Differential Geometry, being a…

A simple geometric construction giving acceptable approximations to the locations of twelve points for placing frets on a guitar is described both geometrically and analytically. (DT)

Considers the electrostatic problem of a point charge in a domain bounded by conducting planes. Lists all such domains for which a solution by images exists, describes the image charge arrays in familiar crystallographic terms, and gives an illustrative example. (Author/GS)

Describes an analysis of the direction taken by a baseball immediately after coming into contact with the bat. Uses geometry, trigonometry, and physics. (MKR)

Tensile and compressive forces in planar trusses can be analyzed using either the method of sections or the method of joints. This article summarizes and extends a project accomplished by a high school student using the method of joints and graphing calculators, spreadsheets, and matrix-manipulation software. (MKR)

Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include directed line segments, applications to geometry, vectors and scalars, components, inner product,…

The author recommends the use of flow charting to help students understand the manipulation of algebraic formulae. He identifies some problems with flow charts and suggests an alternative method of constructing flow diagrams. (SD)

Shows, by a judicious exploitation of the Runge-Lenz vector, that the Kepler initial value problem is endowed with a nice geometric structure which enables one to determine, after a single trivial arithmetic calculation, the orbit associated with any given set of initial data. (Author/GA)

The simple physics behind the mechanism of the toy are explained. Experimental and mathematical steps are given that help in understanding the motion of the doll-pair. The geometry of the setup is described. (KR)

Presents activities that combine astronomy problems with algebra, geometry, trigonometry, data analysis, and physics. Provides experiences for students in making distance measurements themselves by using the method of parallax. (ASK)

A particular shot on a pool table is analyzed using the concept of similar triangles, to introduce the equivalence of the "incident-reflection" principle and the "minimum-distance" principle. (CR)

An application of transformation geometry to special relativity is described. No knowledge of physics is required, but the application uses transformation ideas in a nontrivial way. A comparison is given of reflections in the Euclidean and Minkowski (non-Euclidean) planes. (MNS)