Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order…

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…

Introductory physics courses can be a challenge for some college students, especially those that have not taken Advanced Placement (AP) physics courses in high school. Even some classical mechanics concepts, such as energy, power, or the laws of Newton, can be non-intuitive and hard to grasp. When it comes to evaluating the learning outcome of our…

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

In "How to Solve It", accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to…

The circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of geometry and mathematical physics, optics, and electricity. Here we discuss two of its applications: localizing an object in space and calculating electric fields. First, we…

Describes a hand held calculator exercise for computing the Rydberg Constant accurately. (SL)

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)