The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

This article describes an alternate way to utilize a circular model to represent thirds by incorporating areas of circular segments, trigonometric functions, and geometric transformations. This method is appropriate for students studying geometry and trigonometry at the high shool level. This task provides valuable learning experiences that…

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)

Describes an analysis of the direction taken by a baseball immediately after coming into contact with the bat. Uses geometry, trigonometry, and physics. (MKR)

Computer graphics are used to display the sum of the first few terms of the series solution for the problem of the vibrating string frequently discussed in introductory courses on differential equations. (MNS)

Describes a project in which trigonometry and precalculus students cooperate to measure the height of an inaccessible water tower. (MKR)

An application of trigonometry in weather forecasting, dealing with cloud height, is discussed. (MNS)

Presented are five short articles which describe innovations in mathematics teaching. Included are "Polar Summation,""The Age of the Solar System,""Forward Homework--A Motivational Tool,""Trigonometric Identities through Calculus," and "Algorithms for Evaluation of Polynomials." (CW)

A discussion of the mathematics of rugby is related to an earlier article about mathematics and the physical world. (MP)

Describes Kerf bending which is used to produced a curved shape out of plywood. Discusses why Radtke's kerf-cut method yields a circular arch. (KHR)

Formulas for use in computer programs are presented. Two programming applications are discussed: one to ballistics using inverse sine and one to hours of daylight using inverse cosine. (MNS)

Presents activities that combine astronomy problems with algebra, geometry, trigonometry, data analysis, and physics. Provides experiences for students in making distance measurements themselves by using the method of parallax. (ASK)

Considers a trigonometric solution to a standard calculus minimization problem. Presents a geometric solution which can be used to solve other trigonometric or algebraic problems. (PK)

The Center for Occupational Research and Development (CORD) developed an applied mathematics course that integrates algebra, geometry, trigonometry, and other strands; centers around hands-on laboratory experiences; and uses real-world problems found in the world of work. (MKR)

Presents a problem in which the incorrect application of the Law of Sines leads to an erroneous solution. Demonstrates that the commission of this error by an ophthalmologist using laser trabeculoplasty could lead to patient injury. (MDH)