Symmetry and invariance play a fundamental role in modern physics and related disciplines, and students entering a STEM field need practice with symmetry-based arguments as part of the preparation for their future careers. We refer to symmetry based solutions as those that either make use of the existing geometric symmetry in a problem to simplify…

Mathematical reasoning with algebraic and geometric representations is essential for success in upperdivision and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to…

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community's social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic,…

In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close…

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

Mental-rotation ability modestly predicts chemistry achievement. As such, sex differences in mental-rotation ability have been implicated as a causal factor that can explain sex differences in chemistry achievement and degree attainment. Although there is a correlation between mental-rotation ability and chemistry achievement, laboratory and field…

A method is proposed to simplify analytical computations of the transfer function for electrical circuit filters, which are made from repetitive identical stages. A method based on the construction of Pascal's triangle is introduced and then a general solution from two initial conditions is provided for the repetitive identical stage. The present…

Dimensional analysis, superposition principle, and continuity of electric potential are used to study the electric potential of a uniformly charged square sheet on its plane. It is shown that knowing the electric potential on the diagonal and inside the square sheet is equivalent to knowing it everywhere on the plane of the square sheet. The…

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

We present a derivation for the coordinates of the centre of mass--or centre of gravity--of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the…

An account of peculiar light patterns produced by reflection in a pool under falling rain droplets was recently reported by Molesini and Vannoni (2008 Eur. J. Phys. 29 403-11). The mathematical approach, however, only covered the case of a symmetrical location of a light source and the observer's eyes with respect to the vertical of the falling…

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…

We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual Biot-Savart law of magnetostatics gives the correct magnetic field of the problem. We also show…

This introductory activity explores the advantages of different roof shapes for different climates or situations. It addresses questions such as "When you walk or drive around your neighborhood, what do the roofs look like?" and "What if you lived in an area with a different climate, how would that affect the style of roof that you might find?"…

Some applications of ratio and proportion to scale drawing involving geometric figures are given. The activities or problems concern the earth and space, scale speeds, and the earth-moon system. (MNS)