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…

Logarithmic spirals are among the most fascinating curves in the plane, being the only curves that are equiangular, and the only ones that are self-similar. In this article, we show that in three dimensions, these two properties are independent. Although there are surfaces that have both properties, there are some that are equiangular, but not…

In this paper, some new results related to the integral mean value theorem are proven. This paper includes a discussion of Flett's Mean Value Theorem. (Contains 2 figures.)

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…

The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…

Spatial reasoning is a skill that needs to be developed in students as it is important in geometry for determining total surface areas and volumes of 3-dimensional shapes (Liedtke, 1995). Simply teaching children the formulae, in this case for finding total surface areas, can limit them in understanding mathematics conceptually (Bonotto, 2003).…

This article examines important geometric concepts embedded in the shape and design of natural and manufactured objects. The Whitins first describe fourth graders exploring why manhole covers are circles. Then the authors offer a range of activities to demonstrate how inquiring about shape in botany, geology, biology, and industry can effectively…

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)