From a geometry course for prospective teacher, several methods for dividing a circle into three parts using only Euclidean geometry are explored.

Building on their knowledge of the three possible outcomes of solving 2x2 systems of equations, students use three-dimensional geometric figures to investigate the eight possible outcomes for solving 3x3 systems of equations.

Real numbers are often a missing link in mathematical education. The standard working assumption in calculus courses is that there exists a system of "numbers", extending the rational number system, adequate for measuring continuous quantities. Moreover, that such "numbers" are in one-to-one correspondence with points on a "number line". But…

The authors hope to show how a geometric insight can add to the richness of our students' experiences when they first encounter the solutions to two equations in two unknowns.

Discusses early Euclidean cosmologies, inadequacies in classical Euclidean cosmology, and the development of non-Euclidean cosmologies. Explains the present state of the theory of cosmology including the work of Dirac, Sandage, and Gott. (CP)

By introducing elementary trigonometry earlier in a geometry course, a teacher can demonstrate how a variety of techniques can be brought to bear on the same problem. Eight theorems illustrate this. (Author/KM)

Providing for original and creative thinking by geometry students is discussed. Techniques for discovering theorems are suggested, and examples of places in geometry where these methods can be used are given. (DT)

The mathematics involved in a practical application of matrices and vectors to the field of computer graphics where three-dimensional objects are moved and displayed is explained. (DT)

This textbook provides the foundation for a course in mathematics covering arithmetic, algebra, geometry, conic sections, and arithmetic of infinites. An appendix on practical gauging is included, as well as a supplement containing the history of logarithms. [This edition was corrected and improved by Samuel Clark.]

THIS PAPER IS CONCERNED WITH GRAPHIC PRESENTATION AND ANALYSIS OF GROUPED OBSERVATIONS. IT PRESENTS A METHOD AND SUPPORTING THEORY FOR THE CONSTRUCTION OF AN AREA-CONSERVING, MINIMAL LENGTH FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM. TRADITIONALLY, THE CONCEPT OF A FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM HAS REFERRED TO THAT…

Reported is a study in the Oakleaf Elementary School to test the hypothesis that variability of achievement within a particular grade approximates the number of years the pupils have been in school (e.g., in the third grade, a spread of three years is expected). Data were collected and analyzed regarding range of achievement prior to instruction…

The material in this booklet is concerned with a discussion and examination of geometric puzzles and the ideas which result from their study. The general idea of graphs is introduced as a tool which can be used to solve geometric puzzles. The fact that working with puzzles can lead to unexpected mathematical discoveries is stressed. Such topics as…