This paper describes the genesis and purpose of our geometry methods course, focusing on a geometry-teaching technology we created using NVIDIA[R] Chameleon demonstration. This article presents examples from a sequence of lessons centered about a 3D computer graphics demonstration of the chameleon and its geometry. In addition, we present data…

MATERIALS ARE INTENDED FOR A UNIFIED AND ACCELERATED PLANE AND SOLID GEOMETRY COURSE AND FOR EASY MODIFICATION AND ADAPTATION BY EXPERIENCED OR INEXPERIENCED TEACHER. TEXTBOOKS TO WHICH THE GUIDE HAS BEEN KEYED ARE LISTED. UNITS ARE GIVEN FOR BOTH SEMESTERS WITH TIME ALLOTMENTS RECOMMENDED. EACH UNIT IS SUBDIVIDED INTO TOPICS AND OBJECTIVES,…

The length of the longest ladder which will go round a right-angled bend in a corridor is found by five methods, none of which involves calculus. (MM)

In this article, we investigate the construction of spirals on an equilateral triangle and prove that these spirals are geometric. In further analysing these spirals we show that both the male (straight line segments) and female (curves) forms of the spiral exhibit exactly the same growth ratios and that these growth ratios are constant…

A complex technology-based problem in visualization and computation for students in calculus is presented. Strategies are shown for its solution and the opportunities for students to put together sequences of concepts and skills to build for success are highlighted. The problem itself involves placing an object under water in order to actually see…

We solve two problems that arise when constructing picture frames using only a table saw. First, to cut a cove running the length of a board (given the width of the cove and the angle the cove makes with the face of the board) we calculate the height of the blade and the angle the board should be turned as it is passed over the blade. Second, to…

A crystal model laboratory exercise is presented that allows students to examine relations among the microscopic-macroscopic-symbolic levels, using crystalline mineral samples and corresponding crystal models. Students explore the relationship between solid-state structure and crystal form. Other structure-property relationships are explored. The…

We explored the effects of task-related factors on reasoning processes in geometry focusing on a comparison-of-perimeters task in which the irrelevant feature area interferes with the reasoning process. We studied the effects of congruity, salience, and complexity on participants' accuracy of responses and reaction times. The study shows that…

We examined the recollections by first-year technical college students of concepts in Descriptive Geometry four months after they had studied the subject; furthermore, we compared the relative efficiency between group of students who had been helped in their studies by computer programs and those who had used the traditional paper-and-pencil…

We investigated how human adults orient in enclosed virtual environments, when discrete landmark information is not available and participants have to rely on geometric and featural information on the environmental surfaces. In contrast to earlier studies, where, for women, the featural information from discrete landmarks overshadowed the encoding…

Prague, as many people will know, is a beautiful and very accessible city with many architectural gems. One of its lesser-known features is its architectural link with cubism. These include a remarkable streetlamp hidden in a small square, Jungmannovo namesti, just a stone's throw from the main Mustek metro station at the top of Wenceslas Square…

A method is given for the analysis of geodesic domes involving plane geometry. The method shows how to calculate all necessary angles and chords, given the length of one side. (MP)

An investigation using the Pythagorean theorem, the area of a triangle, and some first-year algebra yields a relationship between the radii of inscribed and escribed circles. (MP)

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 study analyzes measurement learning expectations involving area and volume in grades 1-8 across several U.S. states and high-performing TIMSS Asian countries, including Singapore, Taiwan, and Japan. Based on a review of official curriculum documents, results of this study indicate that the mathematics content, grade placement, and cognitive…