Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)

In this article, a continuation of SE 513 148, the author presents seven additional applications of group theory to high school mathematics. These applications can be used, not only to illustrate the group concept, but also to extend the development of ideas in the high school curriculum. (SD)

This textbook is a third-year high school mathematics course and is the third of the series of textbooks on secondary mathematics. It completes the study of high-school algebra, trigonometry, and solid geometry. The features of this course are: (1) Reviews are carried on at frequent intervals throughout the course; (2) At the end of each chapter…

A class of triangles related to the Pythagorean triangles is described; theorems concerning this class are proved. (SD)

The author argues that sine, secant, and tangent should be taught as the three basic trigonometric functions rather than sine, cosine, and tangent. (SD)

Describes the college-level course offered at the State University of New York, which combines plane geometry and plane trigonometry. Explains lesson sequences and sample exercises to show how the course develops all of the major principles of geometry and trigonometry using three basic constructions: perpendicularity, angle congruency, and angle…

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

Introduces handling data as conceived by Euclid, which provides some interesting possibilities for students to investigate fundamental geometrical ideas as well as relating some elementary geometry with elementary trigonometry. (ASK)

THIS GUIDE OUTLINES THE MINIMUM MATERIAL FOR WHICH STUDENTS OF NINTH YEAR MATHEMATICS - COURSE 1 - ALGEBRA WERE HELD RESPONSIBLE ON THE REGENTS EXAMINATIONS BEGINNING IN JUNE, 1966. THE REPORT ALSO PRESENTS THE SCOPE AND CONTENT OF THE ALGEBRA COURSE AND POSSIBLE SUGGESTIONS FOR TEACHING THE MATERIAL TO STUDENTS. (RP)

THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE ACTIVITIES ON (1) CONSTRUCTION OF SQUARES, RECTANGLES, TRIANGLES, AND…

Several geometric and trigonometric proofs are discussed. These proofs were selected from a larger group because of their instructional value promoting enrichment or generalization. (SD)

This book presents motivational ways to teach key concepts and topics common to all secondary mathematics curricula. It is arranged by subject matter which includes algebra, geometry, trigonometry, probability, statistics, and miscellaneous topics. The objective to be attained by implementing the unit on each of these subjects is stated, and the…

This article shows how simple instruments may be used to construct angles of certain measures and applies this procedure to more detailed problems. A proof of the Pythagorean Theorem is given using these procedures. (CT)