Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

Dalton's law for gas mixtures provides one method for predicting the pressure-volume-temperature (PVT) behavior of a gas mixture from the PVT behavior of the individual pure gases that comprise it. An attempt is made to separate fact from myth, to enlarge on a treatment of possible cases for application, and to provide contemporary means on…

The first introduction to molecular geometry should be through the simple and easily understood VSEPR model, as the Valence Bond Theory and MO Theory suffer from limitations as far as understanding molecular geometry is concerned. The VSEPR model gives a perfectly satisfactory description of the bonding that follows directly from the Lewis model…

This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

In texts on vector analysis one finds many different methods of proving the vector triple product identity. Most of these rely on complicated geometrical constructions or theorems drawn from vector space theory. The component method is generally regarded as being merely long and tedious. Yet, viewed in the correct way, the component method is…

This article explores the transmission of practical knowledge in the XV and XVI centuries. According to cosmographer Egnatio Danti, optics and other mathematical sciences had "been banished" from the main philosophical schools of his period, and "the little which remains to us is limited to some practical aspects learned from the mechanical…

Formulas presented for the calculation of [Summation of n over j=1] j[superscript k] (n, k [is a member of] N) do not have a closed form; they are in the form of recursive or complex formulas. Here an attempt is made to present a simple formula in which it is only necessary to compute the numerical coefficients in a recursive form, and the…

This article employs the Archimedean method of estimating the value of pi within an inscribed pentagon. We show how to write these approximations in terms of the golden ration.

The article deals with the area of polygons that are inscribed in a given circle. Naturally, the following question arises: Among all n-polygons that are inscribed in a given circle, which one has the biggest area? Intuitively, it may be guessed that is suitable for secondary students, and without any use id calculus, but only using very…

This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

This article explores how different proofs of a solution to the Surfer Problem provide answers to the question "Why"?

This article describes a development of conic surfaces that connects different definitions of the conics. A classroom project using Dandelin Spheres is also described.

This article describes a polyhedra construction project that illustrates how one activity can address several of the mathematics content standards in the NCTM Principles and Standards for School Mathematics.

This article offers some ideas about creating mathematical art based on number patterns. It includes a process for students that integrates number and geometry and results in attractive and useful patterned squares. Students may pursue the activity with paper and pencil or they may use computer software like The Geometer's Sketchpad to achieve…

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…