There is an old saying that "there is more than one way to skin a cat." Such is the case with finding the height of tall objects, a task that people have been approximating for centuries. Following an article in the "Australian Primary Mathematics Classroom" (APMC) with methods appropriate for primary students (Brown, Watson,…

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…

In this article, the authors present a lesson whose goal is to utilise a scientific environment to immerse a trigonometry student in the process of mathematical modelling. The scientific environment utilised during this activity is a physics simulation called "Wave on a String" created by the PhET Interactive Simulations Project at…

We illustrate and discuss the method, called CORDIC, which many hand calculators use to calculate the trigonometric and other functions.

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

Two curious thought experiments concerning the speed of light are presented which have been used to provoke the interest of undergraduate physics students. (Contains 2 figures.)

The Department of Mathematics and Statistics at Utah State University offers two courses for preservice secondary school mathematics teachers that complement each other in working toward a vision for school mathematics in which "all students have access to high-quality, engaging mathematics instruction." Through these courses, students…

This paper describes a medieval instrument, a "quadrans novus", which turned up during archaeological works in England. The invention of the instrument by Profacius in 1288 is discussed in terms of two other medieval instruments, the "quadrans vetus" and the common astrolabe. The characteristics of the present instrument are compared with those of…

Story problems are a part of most mathematics curricula and are sometimes used as writing exercises in mathematics classrooms. Such writing exercises may include requiring students to rewrite story problems in their own words, using language that is familiar to them, or rewriting story problems using simpler number facts. The current emphasis on…

By using an identity relating to Bernoulli's numbers and power series expansions of cotangent function and logarithms of functions involving sine function, cosine function and tangent function, four inequalities involving cotangent function, sine function, secant function and tangent function are established.

This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…

The K-W-L method of teaching is a simple method that actively engages students in their own learning. It has been used with kindergarten and elementary grades to teach other subjects. The authors have successfully used it to teach physics at the college level. In their introductory physics labs, the K-W-L method helped students think about what…

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)

This note gives an alternative formulation of Euler's formula.