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…

Recently a teacher friend enquired about the S-I-R equations for disease spread, and what follows was stimulated by that exchange. COVID-19 provides an opportunity to put mathematical flesh on verbal bones such as "self-isolation", "lockdown", "herd immunity", "flattening the curve", "closed…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Describes several ways to partially levitate permanent magnets. Computes field line geometries and oscillation frequencies. Provides several diagrams illustrating the mechanism of the oscillation. (YP)

Addresses the principles and problems associated with the use of significant figures. Explains uncertainty, the meaning of significant figures, the Simple Rule, the Three Rule, and the 1-5 Rule. Also provides examples of the Rules. (ML)

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

The dynamics of some common sports, such as race walking, running, cycling, jumping, and throwing, are presented. Rough estimates of the relevant physical quantities required for these individual sports are discussed. General mathematical formulas are derived which can be used for judging the performance of any athlete. (Author/KR)

Proposes a simple procedure based on an expansion of the exponential terms of Raoult's law by applying it to the case of the benzene-toluene mixture. The results with experimental values are presented as a table. (YP)

Describes two activities for developing computational skills, discovering patterns, checking answers, and factoring quadratics and equivalent fractions. Provides worksheets for the activities. (YP)

Presents a calculator-type computer program, CLICAL, in conjunction with complex number, vector, and other geometric algebra computations. Compares the CLICAL with other symbolic programs for algebra. (Author/YP)