Gives a student-accessible proof that, in any convex polyhedron, the number of vertices plus the number of faces is always two more than the number of edges. (MKR)

Recorded are some biographical data about the late professor Freudenthal along with some indications about his mathematical work. In an appendix, a tiny part of his mathematical work which can be explained in a fairly direct manner is discussed. (Author)

Interprets the philosophical concept of warrant in a mathematics education context and applies it to two central questions: (1) in what sense does mathematical proof warrant?; and (2) can there be warrants for mathematical knowledge other then deductive proofs? (Contains 36 references.) (Author/ASK)

Discusses problems similar to the Pythagorean Theorem as they were presented in historical mathematical texts from China and Babylon dating back to well before the time of Pythagoras. (ASK)

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…