Presents situations from geometry classrooms resulting from observations of five geometry teachers and their classes. Concludes that some teachers are influenced by their beliefs, professional development experiences, and views about their own teaching. Contains 11 references. (ASK)

Presents student methods for finding out the number of different squares on a chessboard. Includes extensions of the activity. (MKR)

Gives examples of new mathematics theorems and proofs shown to the author by his students. Reflects on the notion of proof and discusses issues of multiculturalism in mathematics and descriptions of mathematics. (MKR)

Shows how geometric truths can be reinforced by simple exercises with lines and dots. (MKR)

The path taken and the turns made as a turtle traces a polygon are examined to discover an important theorem in geometry. A unique tool, the Angle Adder, is implemented in the investigation. (Contains 9 figures.)

Persistence of Vision Raytracer (POV-Ray), a free computer program for creating photo-realistic, three-dimensional scenes and a link for Mathematica users interested in generating POV-Ray files from within Mathematica, is discussed. POV-Ray has great potential in secondary mathematics classrooms and helps in strengthening students' visualization…

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…

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…

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 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 study examined the improvement of students' comprehension of geometric concepts through analytical writing about their own misconceptions using a reflective tool called an ERNIe (acronym for ERror aNalyIsis). The purpose of this study was to determine whether the ERNIe process could be used to correct geometric misconceptions, as well as how…