We demonstrate the Stirling formula, approximating the factorial, utilising accessible and elementary methods in an engaging manner.

We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

Interesting conservation properties that exist in parallelograms are well known, such as: diagonal intersection, pairs of interior triangles that overlap each other, and other properties. This article presents a dynamic study of choosing any point inside and outside the parallelogram and connecting it with two of the vertices of the parallelogram.…

In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic…

The COVID-19 pandemic has forced the rapid adoption of remote teaching modalities including "hyflex" where students attend some class sessions in person and some online. Managing the hyflex course requires faculty to quickly generate several reports and to update these reports rapidly when the authorities adjust the rules, students…

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…

There is a close connection between simple harmonic motion and uniform circular motion. This connection is widely taught and included in standard textbooks. Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass-spring system and the centripetal acceleration formula. Previously…

The variation of the period of oscillation of a pendulum with the amplitude is known as "circular error" to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude, but the simple equation due to Denman,…

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…

Functions and formulas in spreadsheets provide an instructional opportunity to help students build their skills in identifying errors in their own work and identifying a path to go about correcting the errors. This paper provides examples of functions and equations used to create two approaches to calculating the solution to one problem, such as a…

Oxidation number (ON) is taught as an electron-counting concept for redox reactions in chemistry curriculum. The molecular formula method, the Lewis formula method, and the structural formula method have all been used to determine ON. However, the task of assigning ON still poses problems for some teachers and students. This paper explores a new…

This article is the fourth in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows an activity demonstrating Euler's Theorem, which gives the distance from between the circumcentre and the incentre of a triangle.

Any quadratic function has a line of symmetry going through its vertex; any cubic function has 1800 rotational symmetry around its point of inflection. However, polynomial functions of degree greater than three can be both symmetrical and asymmetrical (Goehle & Kobayashi, 2013). This work considers algebraic conversions of symmetrical quartic…

In this paper, we first focus on the sum of powers of the first n positive odd integers, T[subscript k](n)=1[superscript k]+3[superscript k]+5[superscript k]+...+(2n-1)[superscript k], and derive in an elementary way a polynomial formula for T[subscript k](n) in terms of a specific type of generalized Stirling numbers. Then we consider the sum of…