In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

College physics textbooks (algebra based) tend to shy away from topics that are usually thought to require calculus. I suspect that most students are just as happy to avoid these topics. Occasionally, I encounter students who are not so easily satisfied, and have found it useful to maintain a storehouse of non-calculus solutions for some common…

In his beautiful paper, Hasan Fakhruddin reported observations of mirror-like reflections in the rough surface of a ground glass plate. Similar effects have been recently employed for metrology of the roughness of optical diffusers used in modern light emitting device illumination systems. We report the observations of specular reflection in…

If an object is conveniently located in front of two plane mirrors placed at an angle, an observer can see a superposition of images that results in a face with three eyes, called in this text a "triclops." The conditions of occurrence of such an image may seem trivial, but this is incorrect: rather, the correct interpretation of this…

A few years ago we began to revamp our introductory physics course for life science students. We knew that this cohort would be less prepared and less adventurous mathematically than engineering, physical science, or mathematics majors. Moreover, from our own experience and the mathematics education literature, we knew that trigonometry would be…

I present a novel way to introduce the lunar orbital eccentricity in introductory astronomy courses. The Moon is perhaps the clearest illustration of the general orbital elements such as inclination, ascending node, eccentricity, perigee, and so on. Furthermore, I like the students to discover astronomical phenomena for themselves, by means of a…

In a previous issue of "The Physics Teacher", John Hubisz explained how a mathematics background check has been used at three different colleges to determine the appropriate physics sequence for incoming students. Based on their performance, students are placed into either calculus-based physics (CBP), algebra-trig physics (ATP), or a year of…

Techniques which use the shadow of the earth as a reference in relation to the angular radii of the sun and moon permit determination of the distance from the earth to the moon. (TS)

Describes an instructional strategy to convey the elements of trigonometry to introductory physics students. (SK)

Describes trigonometric calculations of the "fullness" (as viewed from Earth) of the outer planets as a function of their semi-major axes and their positions relative to Earth and the sun. (WRM)

Describes a homemade experimental chamber constructed to accurately measure the refractive index of a transparent liquid. (MDH)

Utilizes vector mathematics to explain the reflective properties of a corner cube retroreflector, consisting of three plane mirrors assembled at right angles with a common vertex. Analyzes the useful property that an incident beam of light at any point in this reflector will return on a parallel path. (MDH)

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

Presents a problem to determine conditions under which two identical masses, constrained to move along two perpendicular wires, would collide when positioned on the wires and released with no initial velocity. Offers a solution that utilizes the position of the center of mass and a computer simulation of the phenomenon. (MDH)