A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.

Based on relativistic velocity addition and the conservation of momentum and energy, I present simple derivations of the expressions for the relativistic momentum and kinetic energy of a particle, and for the formula E = mc[superscript 2]. (Contains 5 footnotes and 2 figures.)

An introductory approach to black holes is presented along with astronomical observational data pertaining to the presence of a supermassive black hole at the center of our galaxy. Concepts of conservation of energy and Kepler's third law are employed so students can apply formulas from their physics class to determine the mass of the black hole…

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…

The global positioning system (GPS) provides an excellent educational example of how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The authors…

In this note the authors investigate ways to shorten the amount of work involved in using the Rational Roots Theorem to find the rational roots of a polynomial with integral coefficients. The first result is a proof of a fact that we had long suspected, but were never able to find the statement of in any of the college algebra textbooks we had…

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)