These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

The story is often told of the calculation by G.I. Taylor of the yield of the first ever atomic bomb exploded in New Mexico in 1945. It has indeed become a staple of the classroom whenever dimensional analysis is taught. However, while it is true that Taylor succeeded in calculating this figure at a time when it was still classified, most versions…

In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

A standard example used in introductory combinatoric courses is to count the number of five-card poker hands possible from a straight deck of 52 distinct cards. A more interesting problem is to count the number of distinct hands possible from a Pinochle deck in which there are multiple, but obviously limited, copies of each type of card (two…

The formula [image omitted] is closely related to combinatorics through an elementary geometric exercise. This approach can be expanded to the formulas [image omitted], [image omitted] and [image omitted]. These formulas are also nice examples of showing two approaches, one algebraic and one combinatoric, to a problem of counting. (Contains 6…

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…

The estimate of the time since death and, thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner's cases, especially those that involve criminal or insurance investigations. It has been known almost from the beginning of time that bodies cool after the internal…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

A group of mathematicians and mathematics educators are collaborating in the fine-grained examination of selected "slices" of video recordings of lectures, drawing on Schoenfeld's Resources, Orientations and Goals framework of teaching-in-context. In the larger project, we are exploring ways in which this model can be extended to examine…