There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention within the literature: the spatial distributions of TSP and MST-P stimuli. First, we describe a method for quantifying the relative degree of…

An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…

This booklet contains suggestions for developing six of the twenty topics recommended for students in Secondary Forms III and IV in the schools of Victoria, Australia. These suggestions are intended for students for whom the standard course is unsuitable because of subject time allotments, ability levels, or vocational or educational needs. The…