The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)

Includes short discussion of perimeters of regular polygons having fixed areas, Fibonacci numbers, triangle transformations, transformational matrices, round-off errors, and a mathematical model for musical keys. (RS)

Representation of integers in various bases is explored, with a proof. (MNS)

Presented is an account of some of the activities in mathematics that were carried on during World War II in the United States and comments on their impact on the development of mathematical sciences. (MP)

A short account is given of the Coxeter Symposium on geometry. Included are brief descriptions of selected sessions and a description of a touchable geometry display. (MK)

Discussed are two Euclidean constructions (synthetic approach and coordinate method) to inscribe regular polygons of 5 and 17 sides in a circle. Each step of the constructions is described using diagrams and mathematical expressions. (YP)

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Examines whether the embodiment of a familiar geometric system facilitates better understanding of the vector-space concept than the embodiment of a variety of unfamiliar algebraic systems. Analyzes students' responses with description, final answer, and justification of answers. Provides six problems. (YP)

This study investigated the effectiveness of collaboration between college lecturers and student peers in assessing the instructional practice of in-service student teachers (ISTs). The study was inspired by criticisms that college lecturers' assessments were not producing valid critiques of ISTs' mathematical and pedagogical competencies to…

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)

A controversy in the college-level business arithmetic or business mathematics course is whether the vehicle for learning the subject matter of the course should be algebra or arithmetic. (Author)

Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…