An elementary method to calculate the area, centroid and volume of rotation of the Koch curve is presented. Classroom extensions are provided to allow students to investigate the method used.

Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

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…

We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the previous results to determine the quadratic factors of polynomials over commutative coefficient rings and, in particular, to completely factorize in Z[x] any…

In this paper, we present a novel solution of the quadrature of a parabola based on application of Ramanujan's formula for the partial sum of the square roots of the first "n" natural numbers. We also derive a new formula for calculating of area of a parabolic segment and we apply the result to a generalization of some classical theorems…

The article shows that even a small number of iterations give a very large length of the Koch Curve. The overall purpose of this work is to show that even a small number of iterations can give a very complex fractal structure. In this case it is the very big length of Koch's curve. As examples, the distance from the Earth to the Moon and from the…

In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in R[superscript 3]. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard…

A correlation coefficient taking positive values is introduced. It is more easily understood than other correlation measures especially in social science contexts. Estimation issues are addressed. A data application is given.

In the article 'How Long Is My Toilet Roll--A Simple Exercise in Mathematical Modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a…

The following article deals with the possibility of discovering several parameters of the picture when using Google Maps images, e.g. time and date of taking the image. This is possible with all pictures in which buildings, trees, poles ('objects') can be seen with their shadows. In some cases, one can find -- with a bit of luck -- an aircraft…

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers' estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the…

In this study, we propose an integrated hierarchical model of computational estimation strategies (IHMCES), which can be used to organize a set of computational estimation strategies, used by a group of individuals, in strategy ranges. IHMCES can be used for the description of the repertoire, profile and flexibility of individuals regarding the…

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

This article attempts to identify the kind of arguments that lower secondary school-level pupils use when they apply programming to solve a mathematical problem. By analyzing the data from one group of three pupils working together with Processing (Processing is a Java based tool primarily to learn programme visual effects supported and…