The authors take a mathematical journey into polygonal chains to provide an algorithm that will construct a closed polygonal chain where the lines intersect exactly an exactly an odd number of times.

The sample mean is sometimes depicted as a fulcrum placed under the Dot plot. We provide an alternative geometric visualization of the sample mean using the empirical cumulative distribution function or the cumulative histogram data.

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

A shape grammar is a formalism that has been widely applied, in many different fields, to analyzing designs. Computer implementation of a shape grammar interpreter is vital to both research and application. However, implementing a shape grammar interpreter is hard, especially for parametric shapes defined by open terms. This dissertation…

The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

Pre-existing misconceptions are serious impediments to learning in mathematics. Means for detecting and correcting them have received much attention in the literature of educational research. Dynamic geometry software has been tried at different grade levels. This quasi-experimental study investigates the effect of Cabri-assisted instruction on…

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

There has been a lot of material written about logarithmic spirals of golden proportion but this author states that he has never come across an article that states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles. In this article, the author intends to develop such an equation. (Contains 5…

This column contains brief notes on graphing in three dimensions; patterns in Pascal's triangle; plotting graphs by computer; and an application of the hypocycloid. (MM)

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

Curve-stitching the parabola is used as a means of confirming many of the parabola's mathematical properties and to construct some visually stimulating designs. (MP)