When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…

A definition is given for curves parallel to a closed curve. Equations for inner and out elliptic parallels are derived and explained. (RS)

The authors answer conclusively the question of how certain regular polygons can be "fitted together" around a point in the plane. Proofs lead to the establishment of seventeen cases. (JP)

References to approximations of pi in the Bible and calculations of pi in the Egyptian Phind Papyrus are noted, followed by a finding of an eighteenth-century Polish rabbi about the exactness of the Biblical computation. (MNS)

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12-15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). "Cabri-Geometry (software)," Universite de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct:…

This is the fifth in a series of articles of mathematical paper-folding recreations. Presented are instructions for folding a circular disc to produce regular polygons. (JP)

Given two interesecting lines, the "pencil" of this interesection is the family of all lines passing through the point of intersection. Presented is a characterization of all lines both in the plane and lying in opposite sectors of the plane as determined by one of the original intersecting lines. (JP)